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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

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Chapter
Section
BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 9.4, Problem 21PS
Textbook Problem
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For Problems 19 26 , show that ( f g ) ( x ) = x and ( g f ) ( x ) = x for each pair of functions. (Objective 1)

f ( x ) = 4 x + 2 and g ( x ) = x 4 4

To determine

To check:

The relation (fg)(x)=x=(gf)(x) for the given pair of functions.

Explanation of Solution

Procedure used:

The composition of function f and g is defined by (fg)(x)=f(g(x)), for all x in the domain of g such that g(x) is the domain of f and (gf)(x)=g(f(x)), for all x in the domain of f such that f(x) is the domain of g.

Given:

The given functions are,

f(x)=4x+2

g(x)=x24

Calculation:

The functions are given by,

f(x)=4x+2(1)

g(x)=x24(2)

The composition of function f and g is given by,

(fg)(x)=f(g(x))(3)

(gf)(x)=g(f(x))(4)

Substitute x24 for g(x) in equation (3).

(fg)(x)=f(x24)(5)

Substitute x24 for x in equation (1)

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Chapter 9 Solutions

Intermediate Algebra
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Ch. 9.1 - For Problems 110, specify the domain and the range...Ch. 9.1 - For Problems 110, specify the domain and the range...Ch. 9.1 - For Problems 110, specify the domain and the range...Ch. 9.1 - For Problems 110, specify the domain and the range...Ch. 9.1 - For Problems 110, specify the domain and the range...Ch. 9.1 - For Problems 110, specify the domain and the range...Ch. 9.1 - For Problems 110, specify the domain and the range...Ch. 9.1 - For Problems 110, specify the domain and the range...Ch. 9.1 - For Problems 110, specify the domain and the range...Ch. 9.1 - For Problems 110, specify the domain and the range...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problems 1136, specify the domain for each of...Ch. 9.1 - For Problems 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problem 1136, specify the domain for each of...Ch. 9.1 - For Problems 1136, specify the domain for each of...Ch. 9.1 - For Problems 1136, specify the domain for each of...Ch. 9.1 - For Problems 1136, specify the domain for each of...Ch. 9.1 - For Problems 1136, specify the domain for each of...Ch. 9.1 - For Problems 1136, specify the domain for each of...Ch. 9.1 - For Problems 1136, specify the domain for each of...Ch. 9.1 - For Problems 1136, specify the domain for each of...Ch. 9.1 - For Problems 1136, specify the domain for each of...Ch. 9.1 - If f(x)=5x2, find f(0), f(2), f(1), and f(4).Ch. 9.1 - If f(x)=3x4, find f(2), f(1), f(3), and f(5).Ch. 9.1 - If f(x)=12x34, find f(2), f(0), f(12), f(23).Ch. 9.1 - If g(x)=x2+3x1, find g(1), g(1), g(3), and g(4).Ch. 9.1 - If g(x)=2x25x7, find g(1), g(2), g(3), and g(4).Ch. 9.1 - If h(x)=x23, find h(1), h(1), h(3), and h(5).Ch. 9.1 - If h(x)=2x2x+4, find h(2), h(3), h(4), and h(5).Ch. 9.1 - If f(x)=x1, find f(1), f(5), f(13), and f(26).Ch. 9.1 - If f(x)=2x+1, find f(3), f(4), f(10), and f(12).Ch. 9.1 - If f(x)=3x2, find f(3), f(0), f(1), and f(5).Ch. 9.1 - If f(x)=4x+3, find f(1), f(1), f(3), and f(6).Ch. 9.1 - If f(x)=2x+7, find f(a), f(a+2), and f(a+h).Ch. 9.1 - If f(x)=x27x, find f(a), f(a3), and f(a+h).Ch. 9.1 - If f(x)=x24x+10, find f(a), f(a4), and f(a+h).Ch. 9.1 - If f(x)=2x2x1, find f(a), f(a+1), and f(a+h).Ch. 9.1 - If f(x)=x2+3x+5, find f(a), f(a+6) and f(a+1).Ch. 9.1 - If f(x)=x22x7, find f(a), f(a2) and f(a+7).Ch. 9.1 - If f(x)=2x27 and g(x)=x2+x1, find f(2), f(3), g(4)...Ch. 9.1 - If f(x)=5x22x+3 and g(x)=x2+4x5, find f(2), f(3),...Ch. 9.1 - If f(x)=|3x2| and g(x)=|x|+2, find f(1), f(1),...Ch. 9.1 - If f(x)=3|x|1 and g(x)=|x|+1, find f(2), f(3),...Ch. 9.1 - For Problems 5865, find f(a+h)f(a)h for each of...Ch. 9.1 - For Problems 5865, find f(a+h)f(a)h for each of...Ch. 9.1 - For Problems 5865, find f(a+h)f(a)h for each of...Ch. 9.1 - For Problems 5865, find f(a+h)f(a)h for each of...Ch. 9.1 - For Problems 5865, find f(a+h)f(a)h for each of...Ch. 9.1 - For Problems 5865, find f(a+h)f(a)h for each of...Ch. 9.1 - For Problems 5865, find f(a+h)f(a)h for each of...Ch. 9.1 - For Problems 5865, find f(a+h)f(a)h for each of...Ch. 9.1 - Suppose that the cost function for producing a...Ch. 9.1 - The height of a projectile fired vertically into...Ch. 9.1 - In Company S, the profit function for selling n...Ch. 9.1 - Acar rental agency 50 per day plus 0.32 a mile....Ch. 9.1 - The equation A(r)=r2 expresses the area of a...Ch. 9.1 - The equation I(r)=500r expresses the amount of...Ch. 9.1 - The dosage of a pediatric medication depends on...Ch. 9.1 - For an electric car, the number of miles that can...Ch. 9.1 - Are all functions also relations? 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The...Ch. 9.4 - For Problems 110, answer true or false. To find...Ch. 9.4 - For Problems 110, answer true or false. The...Ch. 9.4 - For Problems 110, answer true or false. The domain...Ch. 9.4 - For Problems 110, answer true or false. The...Ch. 9.4 - For Problems 110, answer true or false. If...Ch. 9.4 - For Problems 110, answer true or false. If...Ch. 9.4 - For Problems 110, answer true or false. If f(x)=x1...Ch. 9.4 - For Problems 110, answer true or false. If f(x)=x1...Ch. 9.4 - For Problems 110, answer true or false. If...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - For Problems 1926, show (fg)(x)=x.and (gf)(x)=x...Ch. 9.4 - For Problems 1926, show (fg)(x)=x.and (gf)(x)=x...Ch. 9.4 - For Problems 1926, show that (fg)(x)=x and...Ch. 9.4 - For Problems 1926, show that (fg)(x)=x and...Ch. 9.4 - For Problems 1926, show that (fg)(x)=x and...Ch. 9.4 - For Problems 1926, show that (fg)(x)=x and...Ch. 9.4 - For Problems 1926, show that (fg)(x)=x and...Ch. 9.4 - For Problems 1926, show that (fg)(x)=x and...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.4 - For Problems 2738, determine the indicated...Ch. 9.5 - For Problems 110, answer true or false. 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Explain...Ch. 9.5 - Explain why every non constant linear function has...Ch. 9.5 - The composition idea can also be used to find the...Ch. 9.5 - For Problems 3140, graph the given function, the...Ch. 9.5 - Lets use a graphing calculator to show that...Ch. 9.5 - Use the approach demonstrated in Problem 55 to...Ch. 9.6 - For Problems 15, answer true and false. In the...Ch. 9.6 - For Problems 15, answer true and false. In the...Ch. 9.6 - For Problems 15, answer true and false. Variation...Ch. 9.6 - For Problems 15, answer true and false. Every...Ch. 9.6 - For Problems 15, answer true and false. In joint...Ch. 9.6 - For Problems 610, match the statement of variation...Ch. 9.6 - For Problems 610, match the statement of variation...Ch. 9.6 - For Problems 610, match the statement of variation...Ch. 9.6 - For Problems 610, match the statement of variation...Ch. 9.6 - For Problems 610, match the statement of variation...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - For Problems 1124, find the constant of variation...Ch. 9.6 - Solve each of the following problems. Objectives...Ch. 9.6 - Solve each of the following problems. Objectives...Ch. 9.6 - Solve each of the following problems. Objectives...Ch. 9.6 - Solve each of the following problems. Objectives...Ch. 9.6 - Solve each of the following problems. Objectives...Ch. 9.6 - Solve each of the following problems. Objectives...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Solve each of the following problems. Objective...Ch. 9.S - Specify the domain and range of the relation and...Ch. 9.S - If f(x)=3x22x+1, find f(2).Ch. 9.S - Specify the domain for f(x)=3x22x+1.Ch. 9.S - If f(x)=3x2, find the difference quotient.Ch. 9.S - Graph f(x)=2x+3.Ch. 9.S - The A-Rental Truck company uses the equation...Ch. 9.S - Graph f(x)=2x24x1.Ch. 9.S - Suppose the cost function for producing a...Ch. 9.S - Graph f(x)=|x3|+1.Ch. 9.S - Graph f(x)=x2.Ch. 9.S - Graph f(x)=12x2.Ch. 9.S - Graph f(x)=(x2)22Ch. 9.S - If f(x)=x2 and g(x)=x22x1, find (fg)(x).Ch. 9.S - If f(x)=2x+1 and g(x)=x23x1, find (gf)(2).Ch. 9.S - Identify the graph as the graph of a function or...Ch. 9.S - Identify the graph as the graph of a one-to-one...Ch. 9.S - Given f={(2,3),(1,5),(4,2),(1,7)}, find the...Ch. 9.S - Find the inverse of the function f(x)=3x+5.Ch. 9.S - A persons paycheck varies directly as the number...Ch. 9.S - Suppose the number of hours it takes to clean a...Ch. 9.S - The volume of a cone varies jointly as the height...Ch. 9.CR - For Problems 14, determine if the following...Ch. 9.CR - For Problems 14, determine if the following...Ch. 9.CR - For Problems 14, determine if the following...Ch. 9.CR - For Problems 14, determine if the following...Ch. 9.CR - If f(x)=x22x1, find f(2), f(3), and f(a).Ch. 9.CR - If f(x)=2x4x+2, find f(2), f(1), and f(3a).Ch. 9.CR - For Problems 710, specify the domain of each...Ch. 9.CR - For Problems 710, specify the domain of each...Ch. 9.CR - For Problems 710, specify the domain of each...Ch. 9.CR - For Problems 710, specify the domain of each...Ch. 9.CR - If f(x)=6x+8, find f(a+h)f(a)h.Ch. 9.CR - If f(x)=2x2+x7, find f(a+h)f(a)h.Ch. 9.CR - The cost for burning a 100-watt bulb is given by...Ch. 9.CR - All Items 30 Off Marked Price is a sign in a local...Ch. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - A college math placement test has 50 questions....Ch. 9.CR - An outpatient operating room charges each patient...Ch. 9.CR - For Problems 2533, graph each of the functions....Ch. 9.CR - For Problems 2533, graph each of the functions....Ch. 9.CR - For Problems 2533, graph each of the functions....Ch. 9.CR - For Problems 2533, graph each of the functions....Ch. 9.CR - For Problems 2533, graph each of the functions....Ch. 9.CR - For Problems 2533, graph each of the functions....Ch. 9.CR - For Problems 2533, graph each of the functions....Ch. 9.CR - For Problems 2533, graph each of the functions....Ch. 9.CR - For Problems 2533, graph each of the functions....Ch. 9.CR - Find the coordinates of the vertex and the...Ch. 9.CR - Find two numbers whose sum is 40 and whose product...Ch. 9.CR - Find two numbers whose sum is 50 such that the...Ch. 9.CR - A garden has 60 yards of fencing and wants to...Ch. 9.CR - Suppose that 50 students are able to raise 250 for...Ch. 9.CR - For Problems 3956, graph the functions. f(x)=x32Ch. 9.CR - For Problems 3956, graph the functions. f(x)=|x|+4Ch. 9.CR - For Problems 3956, graph the functions....Ch. 9.CR - For Problems 3956, graph the functions. f(x)=1x4Ch. 9.CR - For Problems 3956, graph the functions. f(x)=xCh. 9.CR - For Problems 3956, graph the functions. f(x)=|x|Ch. 9.CR - For Problems 3956, graph the functions. f(x)=13|x|Ch. 9.CR - For Problems 3956, graph the functions. f(x)=2xCh. 9.CR - For Problems 3956, graph the functions. f(x)=x+12Ch. 9.CR - For Problems 3956, graph the functions. f(x)=x23Ch. 9.CR - For Problems 3956, graph the functions. f(x)=|x2|Ch. 9.CR - For Problems 3956, graph the functions....Ch. 9.CR - For Problems 3956, the graph of functions....Ch. 9.CR - For Problems 3956, the graph of functions....Ch. 9.CR - For Problems 3956, the graph of functions....Ch. 9.CR - For Problems 3956, the graph of functions....Ch. 9.CR - For Problems 3956, the graph of functions....Ch. 9.CR - For Problems 3956, the graph of functions....Ch. 9.CR - For Problems 5761, determine (fg)(x).and (gf)(x)...Ch. 9.CR - For Problems 5761, determine (fg)(x).and (gf)(x)...Ch. 9.CR - For Problems 5761, determine (fg)(x).and (gf)(x)...Ch. 9.CR - For Problems 5761, determine (fg)(x).and (gf)(x)...Ch. 9.CR - For Problems 5761, determine (fg)(x).and (gf)(x)...Ch. 9.CR - For Problems 6264 figures 9.57-9.59, use the...Ch. 9.CR - For Problems 6264 Figures 9.57-9.59, use the...Ch. 9.CR - For Problems 6264 Figures 9.57-9.59, use the...Ch. 9.CR - For Problems 6567 Figures 9.60-9.62, use the...Ch. 9.CR - For Problems 6567 Figures 9.60-9.62, use the...Ch. 9.CR - For Problems 6567 Figures 9.60-9.62, use the...Ch. 9.CR - For Problems 6869, form the inverse function....Ch. 9.CR - For Problems 6869, form the inverse function....Ch. 9.CR - For Problems 7072, find the inverse of the given...Ch. 9.CR - For Problems 7072, find the inverse of the given...Ch. 9.CR - For Problems 7072, find the inverse of the given...Ch. 9.CR - Andrews paycheck varies directly with the number...Ch. 9.CR - The surface area of a cube varies directly as the...Ch. 9.CR - The time it takes to fill an aquarium varies...Ch. 9.CR - The weight of a body above the surface of the...Ch. 9.CR - If y varies directly as x and inversely as z, and...Ch. 9.CR - If y varies jointly as x and the square root of z,...Ch. 9.CT - For the function f(x)=32x2+7x4, determine the...Ch. 9.CT - Determine the domain of the function f(x)=53x.Ch. 9.CT - If f(x)=12x+13, find f(3).Ch. 9.CT - If f(x)=x26x+3, find f(2).Ch. 9.CT - Find the vertex of the parabola f(x)=2x224x69.Ch. 9.CT - If f(x)=3x2+2x5, find f(a+h)f(a)h.Ch. 9.CT - If f(x)=3x+4 and g(x)=7x+2, find (fg)(x).Ch. 9.CT - If f(x)=2x+5 and g(x)=2x2x+3, find (gf)(x).Ch. 9.CT - If f(x)=3x2 and g(x)=2x, find (fg)(x).Ch. 9.CT - For Problems 1012, find the inverse of the given...Ch. 9.CT - For Problems 10-12, find the inverse of the given...Ch. 9.CT - For Problems 10-12, find the inverse of the given...Ch. 9.CT - If y varies inversely as x, and if y=12 when x=8,...Ch. 9.CT - If y varies jointly as x and z, and if y=18 when...Ch. 9.CT - Find two numbers whose sum is 60, such that the...Ch. 9.CT - The simple interest earning by a certain amount of...Ch. 9.CT - For Problems 17-19, use the concepts of...Ch. 9.CT - For Problems 17-19, use the concepts of...Ch. 9.CT - For Problems 17-19, use the concepts of...Ch. 9.CT - For Problems 20-25, graph each function. f(x)=x1Ch. 9.CT - For Problems 20-25, graph each function....Ch. 9.CT - For Problems 20-25, graph each function. f(x)=2x2Ch. 9.CT - For Problems 20-25, graph each function....Ch. 9.CT - For Problems 20-25, graph each function. f(x)=1x+3Ch. 9.CT - For Problems 20-25, graph each function. f(x)=x+2

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