Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus Enhanced with Graphing Utilities
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.25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYUIn Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )=3x+4 ; g(x)= 1 3 ( x4 )In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )=32x ; g( x )= 1 2 ( x3 )In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )=4x8 ; g( x )= x 4 +2In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )=2x+6 ; g( x )= 1 2 x3In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )= x 3 8 ; g(x)= x+8 3In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )= (x2) 2 ; x2 ; g(x)= x +2In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f(x)= 1 x ; g(x)= 1 xIn Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f(x)=x ; g(x)=xIn Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f(x)= 2x+3 x+4 ; g(x)= 4x3 2xIn Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f(x)= x5 2x+3 ; g(x)= 3x+5 12xIn Problems 45-50, the graph of a one-to-one function f is given. Draw the graph of the inverse function f 1 .In Problems 45-50, the graph of a one-to-one function f is given. Draw the graph of the inverse function f 1 .In Problems 45-50, the graph of a one-to-one function f is given. Draw the graph of the inverse function f 1 .In Problems 45-50, the graph of a one-to-one function f is given. Draw the graph of the inverse function f 1 .In Problems 45-50, the graph of a one-to-one function f is given. Draw the graph of the inverse function f 1 .In Problems 45-50, the graph of a one-to-one function f is given. Draw the graph of the inverse function f 1 .49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYUIn Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 2 3+xIn Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 4 2xIn Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 3x x+2In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 2x x1In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 2x 3x1In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 3x+1 xIn Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 3x+4 2x3In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 2x3 x+4In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 2x+3 x+2In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 3x4 x2In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= x 2 4 2 x 2 , x0In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= x 2 +3 3 x 2 x073AYU74AYU75AYU76AYU77AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYU85AYU86AYU87AYU88AYU89AYU90AYU91AYU92AYU93AYU94AYU95AYU96AYU97AYU98AYU99AYU100AYU101AYU102AYU103AYU1AYU2AYU3AYU4AYU5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYU19AYU20AYU21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU63AYU64AYU65AYU66AYU67AYU68AYU69AYU70AYU71AYU72AYU73AYU74AYU75AYU76AYU77AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYU85AYU86AYU87AYU88AYU89AYU90AYU91AYU92AYU93AYU94AYU95AYU96AYU97AYU98AYU99AYU100AYU101AYU102AYU103AYU104AYU105AYU106AYU107AYU108AYU109AYU110AYU111AYU112AYU113AYU114AYU115AYU116AYU117AYU118AYU119AYU120AYU121AYU122AYU123AYU124AYU125AYU126AYU127AYU128AYU129AYUSolve each inequality: (a) 3x782x (pp.A79-A80) (b) x 2 x60 (pp.170-172)Solve the inequality: x1 x+4 0 (pp. 245-247)Solve: 2x+3=9 (pp. A44-A46)The domain of the logarithmic function f( x )= log a x is _______.The graph of every logarithmic function f( x )= log a x , where a0anda1 , passes through three points: ____________, _______, and _________.If the graph of a logarithmic function f( x )= log a x , where a0anda1 , is increasing, then its base must be larger than _____.True or False If y= log a x , then y= a x .True or False The graph of f(x)=logax , where a0anda1 , has an x-intercept equal to 1 and no y-intercept .In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. 9= 3 2In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. 16= 4 2In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. a 2 =1.6In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. a 3 =2.1In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. 2 x =7.2In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. 3 x =4.6In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. e x =8In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. e 2. 2 =MIn Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log 2 8=3In Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log 3 ( 1 9 )=2In Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log a 3=6In Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log b 4=2In Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log 3 2=xIn Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log 2 6=xIn Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. ln4=xIn Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. lnx=4In Problems 27-38, find the exact value of each logarithm without using a calculator. log 2 1In Problems 27-38, find the exact value of each logarithm without using a calculator. log 8 8In Problems 27-38, find the exact value of each logarithm without using a calculator. log 5 25In Problems 27-38, find the exact value of each logarithm without using a calculator. log 3 ( 1 9 )In Problems 27-38, find the exact value of each logarithm without using a calculator. log 1/2 16In Problems 27-38, find the exact value of each logarithm without using a calculator. log 1/3 9In Problems 27-38, find the exact value of each logarithm without using a calculator. log 10 10In Problems 27-38, find the exact value of each logarithm without using a calculator. log 5 25 3In Problems 27-38, find the exact value of each logarithm without using a calculator. log 2 4In Problems 27-38, find the exact value of each logarithm without using a calculator. log 3 9In Problems 27-38, find the exact value of each logarithm without using a calculator. ln eIn Problems 27-38, find the exact value of each logarithm without using a calculator. ln e 3In Problems 39—50, find the domain of each function. f(x)=ln(x3)In Problems 39—50, find the domain of each function. g( x )=ln( x1 )In Problems 39—50, find the domain of each function. F(x)= log 2 x 2In Problems 39—50, find the domain of each function. H(x) =log 5 x 3In Problems 39—50, find the domain of each function. f(x)=3 2log 4 ( x 2 5 )In Problems 39—50, find the domain of each function. g(x)=8+5ln(2x+3)In Problems 39—50, find the domain of each function. f(x)=ln( 1 x+1 )In Problems 39—50, find the domain of each function. g(x)=ln( 1 x5 )In Problems 39—50, find the domain of each function. g(x) =log 5 ( x+1 x )In Problems 39—50, find the domain of each function. h( x )= log 3 ( x x1 )In Problems 39—50, find the domain of each function. f( x )= lnxIn Problems 39—50, find the domain of each function. g( x )= 1 lnxIn Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. ln 5 3In Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. ln5 3In Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. ln 10 3 0.04In Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. ln 2 3 0.1In Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. ln4+ln2 log4+log2In Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. log15+log20 ln15+ln20In Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. 2ln5+log50 log4ln2In Problems 51-58, use a calculator to evaluate each expression. Round your answer to three decimal places. 3log80ln5 log5+ln20Find a so that the graph of f( x ) =log a x contains the point ( 2,2 ) .Find a so that the graph of f( x ) =log a x contains the point ( 1 2 ,4 )In Problems 61-64, graph each function and its inverse on the same set of axes. f( x )= 3 x ; f 1 ( x )= log 3 xIn Problems 61-64, graph each function and its inverse on the same set of axes. f(x)= 4 x ; f 1 (x)= log 4 xIn Problems 61-64, graph each function and its inverse on the same set of axes. f(x)= ( 1 2 ) x ; f 1 (x)= log 1/2 xIn Problems 61-64, graph each function and its inverse on the same set of axes. f( x )= ( 1 3 ) x ; f 1 ( x )= log 1/3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y= log 3 x (B) y= log 3 ( x ) (C) y= log 3 x (D) y= log 3 ( x ) (E) y= log 3 ( x1 ) (F) y= log 3 ( x1 ) (G) y= log 3 ( 1x ) (H) y=1 log 3 xIn Problems 65-72, the graph of a logarithmic function is given. Match each graph to one of the following functions: a. y= log 3 x b. y= log 3 ( x ) c. y= log 3 x d. y= log 3 ( x ) e. y= log 3 x-1 f. y= log 3 ( x1 ) g. y= log 3 ( 1x ) h. y=1 log 3 xIn Problems 73-88, use the given function f . 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 )=ln( x+4 )In Problems 73-88, use the given function f . 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 )=ln( x3 )In Problems 73-88, use the given function f . 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+lnxIn Problems 73-88, use the given function f . 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 )=ln( x )In Problems 73-88, use the given function f . 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 )=ln( 2x )3In Problems 73-88, use the given function f . 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 )=2ln( x+1 )In Problems 73-88, use the given function f . 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 )=log( x4 )+2In Problems 73-88, use the given function f . 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 logx5In Problems 73-88, use the given function f . 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 log( 2x )In Problems 73-88, use the given function f . 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 )=log( 2x )In Problems 73-88, use the given function f . 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+ log 3 ( x+2 )In Problems 73-88, use the given function f . 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 log 3 ( x+1 )In Problems 73-88, use the given function f . 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)= e x+2 3In Problems 73-88, use the given function f . 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 x +2In Problems 73-88, use the given function f . 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 x/3 +4In Problems 73-88, use the given function f . 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 x+1In Problems 89-112, solve each equation. log 3 x=2In Problems 89-112, solve each equation. log 5 x=3In Problems 89-112, solve each equation. log 2 (2x+1)=3