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All Textbook Solutions for Precalculus Enhanced with Graphing Utilities
In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. H( x )= 3x6 4 x 2In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. H( x )= 22x x 2 1In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. F( x )= x 2 5x+4 x 2 2x+1In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. F( x )= x 2 2x15 x 2 +6x+9In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. G( x )= x ( x+2 ) 2In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. G( x )= 2x ( x1 ) 2In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. f( x )=x+ 1 xIn Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. f( x )=2x+ 9 xIn Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. f( x )= x 2 + 1 xIn Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. f( x )=2 x 2 + 16 xIn Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. f( x )=x+ 1 x 3In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. f( x )=2x+ 9 x 3In Problems 51-54, find a rational function that might have the given graph. (More than one answer might be possible.)58AYUIn Problems 51-54, find a rational function that might have the given graph. (More than one answer might be possible.)In Problems 51-54, find a rational function that might have the given graph. (More than one answer might be possible.)61AYU62AYU63AYUSolve the inequality 34x5 . Graph the solution set. (pp. A79-A80)Solve the inequality x 2 5x24 . Graph the solution set. (pp. 170-172)Which of the following could be a test number for the interval 2x5 ? (a) 3 (b) 2 (c) 4 (d) 7True or False The graph of f( x )= x x3 is above the x-axis for x0 or x3 , so the solution set of the inequality x x3 0 is { x| x0orx3 } .In Problems 5-8, use the graph of the function f to solve the inequality. (a) f( x )0 (b) f( x )0In Problems 5-8, use the graph of the function f to solve the inequality. (a) f( x )0 (b) f( x )0In Problems 5-8, use the graph of the function f to solve the inequality. (a) f( x )0 (b) f( x )0In Problems 5-8, use the graph of the function f to solve the inequality. (a) f( x )0 (b) f( x )0In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )= x 2 ( x3 ) .In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )=x ( x+2 ) 2 .In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )= ( x+4 ) 2 ( 1x ) .In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )=( x1 ) ( x+3 ) 2 .In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )=2( x+2 ) ( x2 ) 3 .In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )= 1 2 ( x+4 ) ( x1 ) 3 .In Problems 15-18, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 7-10 of Section 4.5.] Solve R( x )0 , where R( x )= x+1 x( x+4 ) .In Problems 15-18, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 7-10 of Section 4.5.] Solve R( x )0 , where R( x )= x ( x1 )( x+2 ) .In Problems 15-18, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 7-10 of Section 4.5.] Solve R( x )0 , where R( x )= 3x+3 2x+4 .In Problems 15-18, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 7-10 of Section 4.5.] Solve R( x )0 , where R( x )= 2x+4 x1 .In Problems 19-48, solve each inequality algebraically. ( x-5 ) 2 ( x+2 )0In Problems 19-48, solve each inequality algebraically. ( x-5 ) ( x+2 ) 2 0In Problems 19-48, solve each inequality algebraically. x 3 -4 x 2 0In Problems 19-48, solve each inequality algebraically. x 3 +8 x 2 0In Problems 19-48, solve each inequality algebraically. 2 x 3 -8 x 2In Problems 19-48, solve each inequality algebraically. 3 x 3 -15 x 2In Problems 19-48, solve each inequality algebraically. ( x-1 )( x-2 )( x-3 )0In Problems 19-48, solve each inequality algebraically. ( x-5 ) 2 ( x+2 )0In Problems 19-48, solve each inequality algebraically. x 3 -2 x 2 -3x0In Problems 19-48, solve each inequality algebraically. x 3 +2 x 2 -3x0In Problems 19-48, solve each inequality algebraically. x 4 x 2In Problems 19-48, solve each inequality algebraically. x 4 9 x 2In Problems 19-48, solve each inequality algebraically. x 4 1In Problems 19-48, solve each inequality algebraically. x 3 1In Problems 19-48, solve each inequality algebraically. x+1 x-1 0In Problems 19-48, solve each inequality algebraically. x-3 x+1 0In Problems 19-48, solve each inequality algebraically. ( x-1 )( x+1 ) x 0In Problems 19-48, solve each inequality algebraically. ( x-3 )( x+2 ) x-1 0In Problems 19-48, solve each inequality algebraically. ( x-2 ) 2 x 2 -1 0In Problems 19-48, solve each inequality algebraically. ( x+5 ) 2 x 2 -4 0In Problems 19-48, solve each inequality algebraically. x+4 x-2 1In Problems 19-48, solve each inequality algebraically. x+2 x-4 1In Problems 19-48, solve each inequality algebraically. 3x-5 x+2 2In Problems 19-48, solve each inequality algebraically. x-4 2x+4 1In Problems 19-48, solve each inequality algebraically. 1 x-2 2 3x-9In Problems 19-48, solve each inequality algebraically. 5 x-3 3 x+1In Problems 19-48, solve each inequality algebraically. x 2 ( 3+x )( x+4 ) ( x+5 )( x-1 ) 0In Problems 19-48, solve each inequality algebraically. x( x 2 +1 )( x-2 ) ( x-1 )( x+1 ) 0In Problems 19-48, solve each inequality algebraically. ( x-5 ) 2 ( x+2 )0In Problems 19-48, solve each inequality algebraically. ( 2-x ) 3 ( 3x-2 ) x 3 +1 0In Problems 49-60, solve each inequality algebraically. ( x+1 )( x-3 )( x-5 )0In Problems 49-60, solve each inequality algebraically. ( 2x-1 )( x+2 )( x+5 )0In Problems 49-60, solve each inequality algebraically. 7x-4-2 x 2In Problems 49-60, solve each inequality algebraically. x 2 +3x10In Problems 49-60, solve each inequality algebraically. x+1 x-3 2In Problems 49-60, solve each inequality algebraically. x-1 x+2 -2In Problems 49-60, solve each inequality algebraically. 3( x 2 -2 )2 ( x-1 ) 2 + x 2In Problems 49-60, solve each inequality algebraically. ( x-3 )( x+2 ) x 2 +3x+5In Problems 49-60, solve each inequality algebraically. 6x-5 6 xIn Problems 49-60, solve each inequality algebraically. x+ 12 x 7In Problems 49-60, solve each inequality algebraically. x 3 -9x0In Problems 49-60, solve each inequality algebraically. x 3 -x0In Problems 61 and 62, (a) find the zeros of each function, (b) factor each function over the real numbers, (c) graph each function by hand, and (d) solve f( x )0 . f( x )=2 x 4 +11 x 3 -11 x 2 -104x-48In Problems 61 and 62, (a) find the zeros of each function, (b) factor each function over the real numbers, (c) graph each function by hand, and (d) solve f( x )0 . f( x )=4 x 5 -19 x 4 +32 x 3 -31 x 2 +28x-12In Problems 63-66, (a) graph each function by hand, and (b) solve . f( x )= x 2 +5x6 x 2 4x+4In Problems 63-66, (a) graph each function by hand, and (b) solve . f( x )= 2 x 2 +9x+9 x 2 4In Problems 63-66, (a) graph each function by hand, and (b) solve . f( x )= x 3 +2 x 2 11x12 x 2 x6In Problems 63-66, (a) graph each function by hand, and (b) solve . f( x )= x 3 6 x 2 +9x4 x 2 +x20For what positive numbers will the cube of a number exceed four times its square?For what positive numbers will the cube of a number be less than the number?What is the domain of the function f( x )= x 4 -16 ?What is the domain of the function f( x )= x 3 -3 x 2 ?What is the domain of the function f( x )= x-2 x+4 ?What is the domain of the function f( x )= x-1 x+4 ?In Problems 73-76, determine where the graph of f is below the graph of g by solving the inequality f( x )g( x ). Graph f and g together. f( x )= x 4 -1 g( x )=-2 x 2 +2In Problems 73-76, determine where the graph of f is below the graph of g by solving the inequality f( x )g( x ). Graph f and g together. f( x )= x 4 -1 g( x )=x-1In Problems 73-76, determine where the graph of f is below the graph of g by solving the inequality f( x )g( x ). Graph f and g together. f( x )= x 4 -4 g( x )=3 x 2In Problems 73-76, determine where the graph of f is below the graph of g by solving the inequality f( x )g( x ). Graph f and g together. f( x )= x 4 g( x )=2- x 2Average Cost Suppose that the daily cost C of manufacturing bicycles is given by C(x)=80x+5000 . Then the average daily cost C is given by C (x)= 80x+5000 x . How many bicycles must be produced each day for the average cost to be no more than 100 ?Average Cost See Problem 77. Suppose that the government imposes a 1000 -per-day tax on the bicycle manufacturer so that the daily cost C of manufacturing x bicycles is now given by C(x)=80x+6000 . Now the average daily cost C is given by C (x)= 80x+6000 x . How many bicycles must be produced each day for the average cost to be no more than 100 ?Bungee Jumping Originating on Pentecost Island in the Pacific, the practice of a person jumping from a high place harnessed to a flexible attachment was introduced to Western culture in 1979 by the Oxford University Dangerous Sport Club. One important parameter to know before attempting a bungee jump is the amount the cord will stretch at the bottom of the fall. The stiffness of the cord is related to the amount of stretch by the equation K= 2W( S+L ) S 2 where W= weight of the jumper (pounds) K= cord’s stiffness (pounds per foot) L= free length of the cord (feet) S= stretch (feet) (a) A 150-pound person plans to jump off a ledge attached to a cord of length 42 feet. If the stiffness of the cord is no less than 16 pounds per foot, how much will the cord stretch? (b) If safety requirements will not permit the jumper to get any closer than 3 feet to the ground, what is the minimum height required for the ledge in part (a)? Source: American Institute of Physics, Physics News Update, No. 150, November 5,1993.Gravitational Force According to Newtons Law of Universal Gravitation, the attractive force F between two bodies is given by F=G m 1 m 2 r 2 where m 1 , m 2 = the masses of the two bodies r= distance between the two bodies G=gravitationalconstant=6.6742 10 11 newtonsmete r 2 kilogra m 2 Suppose an object is traveling directly from Earth to the moon. The mass of Earth is 5.9742 10 24 kilograms, the mass of the moon is 7.349 10 22 kilograms, and the mean distance from Earth to the moon is 384,400 kilometers. For an object between Earth and the moon, how far from Earth is the force on the object due to the moon greater than the force on the object due to Earth? Source: www.solarviews.com;en.wikipedia.orgField Trip Mrs. West has decided to take her fifth grade class to a play. The manager of the theater agreed to discount the regular 40 price of the ticket by 0.20 for each ticket sold. The cost of the bus, 500 , will be split equally among the students. How many students must attend to keep the cost per student at or below 40 ?Make up an inequality that has no solution. Make up one that has exactly one solution.The inequality x 4 +15 has no solution. Explain why.A student attempted to solve the inequality x+4 x3 0 by multiplying both sides of the inequality by x3 to get x+40 . This led to a solution of { x| x4 } . Is the student correct? Explain.Write a rational inequality whose solution set is { x| 3x5 }Evaluate each expression using the graphs of y=f( x ) and y=g( x ) shown in the figure. (a) ( gf )( 8 ) (b) ( fg )( 8 ) (c) ( gg )( 7 ) (d) ( gf )( 5 )In Problems 2 4, for the given functions f and g find: (a) ( fg )( 2 ) (b) ( gf )( 2 ) (c) ( ff )( 4 ) (d) ( gg )( 1 ) f( x )=3x5 ; g( x )=12 x 2In Problems 2 4, for the given functions f and g find: (a) ( fg )( 2 ) (b) ( gf )( 2 ) (c) ( ff )( 4 ) (d) ( gg )( 1 ) f( x )= x+2 ; g( x )=2 x 2 +1In Problems 2 4, for the given functions f and g find: (a) ( fg )( 2 ) (b) ( gf )( 2 ) (c) ( ff )( 4 ) (d) ( gg )( 1 ) f( x )= e x ; g( x )=3x2In Problems 5-7, find fg,gf,ff, and gg for each pair of functions. State the domain of each composite function. f( x )=2x ; g( x )=3x+1In Problems 5-7, find fg,gf,ff, and gg for each pair of functions. State the domain of each composite function. f( x )= 3x ; g( x )=1+x+ x 2In Problems 5-7, find fg,gf,ff, and gg for each pair of functions. State the domain of each composite function. f( x )= x+1 x1 ; g( x )= 1 xIn Problem 8, (a) verify that the function is one-to-one, and (b) find the inverse of the given function. (1,2),(3,5),(5,8),(6,10)In Problem 9, state why the graph of the function is one-to-one. Then draw the graph of the inverse function f 1 . For convenience (and as a hint), the graph of y=x is also given.In Problems 10-13, the function f is one-to-one. Find the inverse of each function and check your answer. State the domain and the range of f and f 1 . f( x )= 2x+3 5x2In Problems 10-13, the function f is one-to-one. Find the inverse of each function and check your answer. State the domain and the range of f and f 1 . f( x )= 1 x1In Problems 10-13, the function f is one-to-one. Find the inverse of each function and check your answer. State the domain and the range of f and f 1 . f( x )= x2In Problems 10-13, the function f is one-to-one. Find the inverse of each function and check your answer. State the domain and the range of f and f 1 . f( x )= x 1/3 +1In Problem 14, f( x ) =3 x andg( x ) =log 3 x Evaluate: (a) f( 4 ) (b) g( 9 ) (c) f( 2 ) (d) g( 1 27 )Convert 5 2 =z to an equivalent statement involving a logarithm.Convert log 5 u13 to an equivalent statement involving an exponent.In Problems 17 and 18, find the domain of each logarithmic function. f( x )=log(3x2)In Problems 17 and 18, find the domain of each logarithmic function. H( x )= log 2 ( x 2 3x+2)In Problems 19-21, evaluate each expression. Do not use a calculator. log 2 ( 1 8 )20REIn Problems 19-21, evaluate each expression. Do not use a calculator. 2 log 2 0.4In Problems 22-25, write each expression as the sum and/or difference of logarithms. Express powers as factors. log 3 ( u v 2 w ),u0,v0,w0In Problems 22-25, write each expression as the sum and/or difference of logarithms. Express powers as factors. log 2 ( a 2 b ) 4 ,a0,b0In Problems 22-25, write each expression as the sum and/or difference of logarithms. Express powers as factors. log( x 2 x 3 +1 ),x0In Problems 22-25, write each expression as the sum and/or difference of logarithms. Express powers as factors. ln ( 2x+3 x 2 3x+2 ) 2 ,x2In Problems 26-28, write each expression as a single logarithm. 3 log 4 x 2 + 1 2 log 4 xIn Problems 26-28, write each expression as a single logarithm. ln( x1 x )+ln( x x+1 )ln( x 2 1 )In Problems 26-28, write each expression as a single logarithm. 1 2 ln( x 2 +1 )4ln 1 2 1 2 [ ln( x4 )+lnx ]Use the Change-of-Base Formula and a calculator to evaluate log 4 19 . Round your answer to three decimal places.Graph y= log 3 x using a graphing utility and the Change-of-Base Formula.In Problems 31-34, use the given function f to: (a) Find the domain of f .(b) Graph f .(c) From the graph, determine the range and any asymptotes of f .(d) Find f 1 , the inverse of f .(e) Find the domain and the range of f 1 (f) Graph f 1 . f( x ) =2 x3In Problems 31-34, use the given function f to: (a) Find the domain of f .(b) Graph f .(c) From the graph, determine the range and any asymptotes of f .(d) Find f 1 , the inverse of f .(e) Find the domain and the range of f 1 (f) Graph f 1 . f( x ) =1+3 xIn Problems 31-34, use the given function f to: (a) Find the domain of f .(b) Graph f .(c) From the graph, determine the range and any asymptotes of f .(d) Find f 1 , the inverse of f .(e) Find the domain and the range of f 1 (f) Graph f 1 . f( x )=3 e x2In Problems 31-34, use the given function f to: (a) Find the domain of f .(b) Graph f .(c) From the graph, determine the range and any asymptotes of f .(d) Find f 1 , the inverse of f .(e) Find the domain and the range of f 1 (f) Graph f 1 . f( x )= 1 2 ln( x+3 )In Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility. 8 6+3x =4In Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility. 3 x 2 +x = 3In Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility. log x 64=3In Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility. 5 x = 3 x+2In Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility. 25 2x = 5 x 2 12In Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility. log 3 x2 =2In Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility. 8=4 x 2 2 5xIn Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility. 2 x 5= 10 xIn Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility. log 6 ( x+3 ) +log 6 ( x+4 )=1In Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility. e 1x =5In Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility. 9 x +4 3 x 3=0Suppose that f( x )= log 2 (x2)+1 . (a) Graph f (b) What is f( 6 ) ? What point is on the graph of f ? (c) Solve f( x )=4 . What point is on the graph of f ? (d) Based on the graph drawn in part (a), solve f( x )0 . (e) Find f 1 ( x ) . Graph f 1 on the same Cartesian plane as f .Amplifying Sound An amplifier’s power output P (in watts) is related to its decibel voltage gain d by the formula P=25 e 0.1d (a) Find the power output for a decibel voltage gain of 4 decibels. (b) For a power output of 50 watts, what is the decibel voltage gain?Limiting Magnitude of a Telescope A telescope is limited in its usefulness by the brightness of the star that it is aimed at and by the diameter of its lens. One measure of a star's brightness is its magnitude; the dimmer the star, the larger its magnitude. A formula for the limiting magnitude L of a telescope, that is, the magnitude of the dimmest star that it can be used to view, is given by L=9+5.1logd where d is the diameter (in inches) of the lens. (a) What is the limiting magnitude of a 3.5inch telescope? (b) What diameter is required to view a star of magnitude 14?Salvage Value The number of years n for a piece of machinery to depreciate to a known salvage value can be found using the formula n= logslogi log( 1d ) where s is the salvage value of the machinery, i is its initial value, and d is the annual rate of depreciation. (a) How many years will it take for a piece of machinery to decline in value from 90,000 to 10,000 if the annual rate of depreciation is 0.20( 20 ) ? (b) How many years will it take for a piece of machinery to lose half of its value if the annual rate of depreciation is 15 ?Funding a College Education A child's grandparents purchase a 10,000 bond fund that matures in 18 years to be used for her college education. The bond fund pays 4 interest compounded semiannually. How much will the bond fund be worth at maturity? What is the effective rate of interest? How long will it take the bond to double in value under these terms?Funding a College Education A child's grandparents wish to purchase a bond that matures in 18 years to be used for her college education. The bond pays 4 interest compounded semiannually. How much should they pay so that the bond will be worth 85,000 at maturity?Estimating the Dale That a Prehistoric Man Died The bones of a prehistoric man found in the desert of New Mexico contain approximately 5 of the original amount of carbon 14. If the half-life of carbon 14 is 5730 years, approximately how long ago did the man die?Temperature of a Skillet A skillet is removed from an oven whose temperature is 450F and placed in a room whose temperature is 70F . Alter 5 minutes, the temperature of the skillet is 400F . How long will it he until its temperature is 150F ?World Population The annual growth rate of the world's population in 2015 was k=1.08=0.0108 . The population of the world in 2015 was 7,214,958,966. Letting t=0 represent 2015, use the uninhibited grow the model to predict the world’s population in the year 2020. Source: U.S. Census BureauRadioactive Decay The half-life of cobalt is 5.27 years. If 100 grams of radioactive cobalt is present now, how much will be present in 20 years? In 40 years?Logistic Growth The logistic growth model Pt= 0.8 1+1.67 e 0.16t represents the proportion of new cars with a global positioning system (GPS). Let t=0 represent 2006, t=1 represent 2007, and so on. (a) What proportion of new cars in 2006 had a GPS? (b) Determine the maximum proportion of new cars that have a GPS. c) Using a graphing utility, graph P=P( t ) . (d) When will 75 of new cars have a GPS?Rising Tuition The following data represent the average in-state tuition and fees (in 2013 dollars) at public four- year colleges and universities in the United States from the academic year 1983 84 to the academic year 2013 14. (a) Using a graphing utility, draw a scatter diagram with academic year as the independent variable. (b) Using a graphing utility, build an exponential model from the data. (c) Express the function found in part (b) in the form A( t )= A 0 e kt . (d) Graph the exponential function found in part (b) or (c) on the scatter diagram. (e) Predict the academic year when the average tuition will reach 12,000 .Wind Chill Factor the following data represent the wind speed (mph) and wind chill factor at an air temperature of 15F . (a) Using a graphing utility, draw a scatter diagram with wind speed as the independent variable. (b) Using a graphing utility, build a logarithmic model from the data. (c) Using a graphing utility, draw the logarithmic function found in part (b) on the scatter diagram. (d) Use the function found in part (b) to predict the wind chill factor if the air temperature is 15nF and the wind speed is 23 mph.Spreading of a Disease Jack and Diane live in a small town of 50 people. Unfortunately, both Jack and Diane have a cold. Those who come in contact with someone who has this cold will themselves catch the cold. The following data represent the number of people in the small town who have caught the cold after t days. (a) Using a graphing utility, draw a scatter diagram of the data. Comment on the type of relation that appears to exist between the days and number of people with a cold. (b) Using a graphing utility, build a logistic model from the data. (c) Graph the function found in part (b) on the scatter diagram. (d) According to the function found in part (b). what is the maximum number of people who will catch the cold? In reality', what is the maximum number of people who could catch the cold? (e) Sometime between the second and third day, 10 people in the town had a cold. According to the model found in part (b). when did 10 people have a cold? (f) How long will it take for 46 people to catch the cold?1CT2CT3CT4CT5CT6CT7CT8CT9CT10CT11CT12CT13CT14CT15CT16CT17CT18CT19CT20CT21CT22CT23CT1CR2CR3CR4CR5CR6CR7CR8CR9CR10CR11CR12CR13CR14CR15CR16CRFind f( 3 ) if f( x )=4 x 2 +5x . (pp. 60-62)Find f(3x) if f(x)=42 x 2 . (pp. 60-62)Find the domain of the function f(x)= x 2 1 x 2 25 . (pp. 64-66)Given two functions f and g , the _____, denoted fg , is defined by (fg)(x)= _____.5AYUTrue or False The domain of the composite function (fg)(x) is the same as the domain of g(x) .In Problems 9 and 10, evaluate each expression using the values given in the table. a. ( fg )( 1 ) b. ( fg )( 1 ) c. ( gf )( 1 ) d. ( gf )( 0 ) e. ( gg )( 2 ) f. ( ff )( 1 )In Problems 9 and 10, evaluate each expression using the values given in the table. a. ( fg )( 1 ) b. ( fg )( 2 ) c. ( gf )( 2 ) d. ( gf )( 3 ) e. ( gg )( 1 ) f. ( ff )( 3 )In Problems 11 and 12, evaluate each expression using the graphs of y=f(x) and y=g(x) shown in the figure. a. ( gf )( 1 ) b. ( gf )( 0 ) c. ( fg )( 1 ) d. ( fg )( 4 )In Problems 11 and 12, evaluate each expression using the graphs of y=f(x) and y=g(x) shown in the figure. a. ( gf )( 1 ) b. ( gf )( 5 ) c. ( fg )( 0 ) d. ( fg )( 2 )In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f( x )=2x ; g( x )=3 x 2 +1In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f( x )=3x+2 ; g( x )=2 x 2 1In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f( x )=4 x 2 3 ; g( x )=3 1 2 x 2In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f( x )=2 x 2 ; g( x )=13 x 2In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f(x)= x ; g(x)=2xIn Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f(x)= x+1 ; g(x)=3xIn Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f(x)=| x | ; g(x)= 1 x 2 +1In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f(x)=| x2 | ; g(x)= 3 x 2 +2In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f(x)= 3 x+1 ; g(x)= x 3In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f(x)= x 3/2 ; g(x)= 2 x+121AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYUIn Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f( x )=2x+3 ; g( x )=3xIn Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f( x )=x ; g( x )=2x4In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f( x )=3x+1 ; g( x )= x 2In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f(x)=x+1 ; g( x )= x 2 +4In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f(x)= x 2 ; g(x)= x 2 +4In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f( x )= x 2 +1 ; g(x)=2 x 2 +3In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f(x)= 3 x1 ; g(x)= 2 xIn Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f(x)= 1 x+3 ; g(x)= 2 xIn Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f(x)= x x1 ; g(x)= 4 xIn Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f(x)= x x+3 ; g(x)= 2 xIn Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f(x)= x ; g(x)=2x+3In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f(x)= x2 ; g(x)=12xIn Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f(x)= x 2 +1 ; g(x)= x1In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f( x )= x 2 +4 ; g(x)= x2In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f(x)= x5 x+1 ; g(x)= x+2 x3In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain of each composite function. f(x)= 2x1 x2 ; g(x)= x+4 2x5In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=2x ; g(x)= 1 2 xIn Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=4x ; g(x)= 1 4 xIn Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )= x 3 ; g(x)= x 3In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=x+5 ; g( x )=x5In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=2x6 ; g( x )=( x+6 )In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=43x ; g( x )=( 4x )In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=ax+b ; g(x)= 1 a (xb) a0In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f(x)= 1 x ; g(x)= 1 xIn Problems 47-52, find functions f and g so that fg=H . H(x)= (2x+3) 4In Problems 47-52, find functions f and g so that fg=H . H(x)= (1+ x 2 ) 3In Problems 47-52, find functions f and g so that fg=H . H(x)= x 2 +1In Problems 47-52, find functions f and g so that fg=H . H(x)= 1 x 2In Problems 47-52, find functions f and g so that fg=H . H(x)=| 2x+1 |In Problems 47-52, find functions f and g so that fg=H . H(x)=| 2 x 2 +3 |59AYU60AYU61AYU62AYU63AYU64AYU65AYU66AYU67AYU68AYU69AYU70AYU71AYU72AYU73AYU74AYU75AYU76AYU77AYUIs the set of ordered pairs { ( 1,3 ),( 2,3 ),( 1,2 ) } a function? Why or why not? (pp. 57-60)Where is the function f( x )= x 2 increasing? Where is it decreasing? (p. 84)What is the domain of f(x)= x+5 x 2 +3x18 ? (pp. 64-66)Simplify: 1 x +1 1 x 2 1 (pp. A39-A41)If x 1 and x 2 are two different inputs of a function f , then f is one-to-one if _____.If every horizontal line intersects the graph of a function f at no more than one point, then f is a(n) ______ function.If f is a one-to-one function and f( 3 )=8 , then f 1 ( 8 )= ________.If f 1 denotes the inverse of a function f , then the graphs of f and f 1 are symmetric with respect to the line _________.If the domain of a one-to-one function f is [ 4, ) , then the range of its inverse function f 1 is ________.True or False If f and g are inverse functions, then the domain of f is the same as the range of g .In Problems 13-20, determine whether the function is one-to-one.In Problems 13-20, determine whether the function is one-to-one.In Problems 13-20, determine whether the function is one-to-one.In Problems 13-20, determine whether the function is one-to-one.In Problems 13-20, determine whether the function is one-to-one. (2,6),(3,6),(4,9),(1,10)In Problems 13-20, determine whether the function is one-to-one. ( 2,5 ),( 1,3 ),( 3,7 ),( 4,12 )In Problems 13-20, determine whether the function is one-to-one. { ( 0,0 ),( 1,1 ),( 2,16 ),( 3,81 ) }In Problems 13-20, determine whether the function is one-to-one. { ( 1,2 ),( 2,8 ),( 3,18 ),( 4,32 ) }In Problems 21-26, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.In Problems 21-26, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.In Problems 21-26, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.