Explanation The given composite function is F ( x ) = ( 2 x + x 2 ) 4 . Name the expression 2 x + x 2 as g ( x ) = 2 x + x 2 . Thus, F ( x ) = ( g ( x ) ) 4 . It can be expressed as F ( x ) = f ( g ( x ) ) as F ( x ) is a composition of f and g . Replace g ( x ) by x to obtain the expression for f ( x ) . Therefore, f ( x ) = x 4 . Hence, it can be concluded that F ( x ) = ( 2 x + x 2 ) 4 can be expressed as F ( x ) = f ( g ( x ) ) , where f ( x ) = x 4 and g ( x ) = 2 x + x 2

Single Variable Calculus: Early Transcendentals, Volume I

8th Edition

ISBN: 9781305270343

Author: James Stewart

Publisher: Cengage Learning

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Chapter 1.3, Problem 43E

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To express: The function F(x)=(2x+x2)4 in the form of (f∘g)(x) .

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Chapter 1.3, Problem 42E

Chapter 1.3, Problem 44E

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Chapter 1 Solutions

Single Variable Calculus: Early Transcendentals, Volume I

Ch. 1.1 - 1. If f(x)=x+2x and g(u)=u+2u, is it true that f =...Ch. 1.1 - If f(x)=x2xx1andg(x)=x is it true that f = g?Ch. 1.1 - The graph of a function f is given. (a) State the...Ch. 1.1 - Prob. 4E Ch. 1.1 - Figure 1 was recorded by an instrument operated by...Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Shown is a graph of the global average temperature...

Ch. 1.1 - Trees grow faster and form wider rings in warm...Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - You place a frozen pie in an oven and bake it for...Ch. 1.1 - Prob. 21E Ch. 1.1 - An airplane takes off from an airport and lands an...Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Evaluate the difference quotient for the given...Ch. 1.1 - Evaluate the difference quotient for the given...Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Sketch the graph of the function. 45. f(x) = x +...Ch. 1.1 - Prob. 46E Ch. 1.1 - Sketch the graph of the function. 47. g(t) = |1 ...Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - Prob. 51E Ch. 1.1 - Prob. 52E Ch. 1.1 - Prob. 53E Ch. 1.1 - Prob. 54E Ch. 1.1 - Prob. 55E Ch. 1.1 - Prob. 56E Ch. 1.1 - Prob. 57E Ch. 1.1 - Prob. 58E Ch. 1.1 - Prob. 59E Ch. 1.1 - Prob. 60E Ch. 1.1 - Prob. 61E Ch. 1.1 - Prob. 62E Ch. 1.1 - Prob. 63E Ch. 1.1 - Prob. 64E Ch. 1.1 - Prob. 65E Ch. 1.1 - Prob. 66E Ch. 1.1 - Prob. 67E Ch. 1.1 - Prob. 68E Ch. 1.1 - Prob. 69E Ch. 1.1 - Prob. 70E Ch. 1.1 - Prob. 71E Ch. 1.1 - Prob. 72E Ch. 1.1 - Prob. 73E Ch. 1.1 - Prob. 74E Ch. 1.1 - Prob. 75E Ch. 1.1 - Prob. 76E Ch. 1.1 - Prob. 77E Ch. 1.1 - Prob. 78E Ch. 1.1 - Prob. 79E Ch. 1.1 - Prob. 80E Ch. 1.2 - Prob. 1E Ch. 1.2 - Prob. 2E Ch. 1.2 - Prob. 3E Ch. 1.2 - Prob. 4E Ch. 1.2 - Prob. 5E Ch. 1.2 - Prob. 6E Ch. 1.2 - Prob. 7E Ch. 1.2 - Prob. 8E Ch. 1.2 - Prob. 9E Ch. 1.2 - Prob. 10E Ch. 1.2 - Prob. 11E Ch. 1.2 - Prob. 12E Ch. 1.2 - Prob. 13E Ch. 1.2 - Prob. 14E Ch. 1.2 - Prob. 15E Ch. 1.2 - Prob. 16E Ch. 1.2 - Prob. 17E Ch. 1.2 - Prob. 18E Ch. 1.2 - Prob. 19E Ch. 1.2 - The monthly cost of driving a car depends on the...Ch. 1.2 - Prob. 21E Ch. 1.2 - For each scatter plot, decide what type of...Ch. 1.3 - Suppose the graph of f is given. 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To express: The function F ( x ) = ( 2 x + x 2 ) 4 in the form of ( f ∘ g ) ( x ) .

Solution Summary: The author explains that the given composite function (x) is a composition of f and g.

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To express: The function F(x)=(2x+x2)4 in the form of (f∘g)(x) .

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Chapter 1 Solutions