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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 17PS
Textbook Problem
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For Problems 1 18 , determine ( f g ) ( x ) .and ( g f ) ( x ) for each pair of functions. Also specify the domain of ( f g ) ( x ) and ( g f ) ( x ) .(Objective 1)

f ( x ) = 3 2 x and g ( x ) = 1 x + 1

To determine

To find:

The composition functions and domain of the given pair of functions.

f(x)=32x and g(x)=1x+1

Explanation of Solution

Given:

The given functions are,

f(x)=32x and g(x)=1x+1.

Approach:

The composition of functions is the process of combining two functions where one function is performed first and the result of which is substituted in place of each x in the other function.

The composition of functions 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.

Method:

To find the domain of the function,

Equating the denominator equal to zero and then find the value of variable. The set of domain of the function is all real number except the finding values.

Calculation:

Consider the given function for f(x),

f(x)=32x….. (1)

Consider the given function for g(x),

g(x)=1x+1……(2)

The composition of function is,

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

Substitute g(x) for x in equation (1).

(fg)(x)=f(g(x))=f(1x+1)=32x+1=3x+32

Thus, the composition function is,

(fg)(x)=3x+32

The domain of fg is given by,

D=(,1)(1,)

Substitute f(x) for x in equation (2)

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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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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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