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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Use the given graphs of f and g to estimate the value of f(g(x)) for x = − 5, − 4, − 3,. . . , 5. Use these estimates to sketch a rough graph of fg.

Chapter 1.3, Problem 54E, Use the given graphs of f and g to estimate the value of f(g(x)) for x =  5,  4,  3,. . . , 5. Use

To determine

To estimate: The value of f(g(x)) for x=5,4,3,2,1,0,1,2,3,4,5 from the graphs of f and g; using these values sketch the graph of fg.

Explanation

First find the value of g(x).

Note that at x=5, the graph g takes the value of −0.2.

Similarly, from the graph g, the values of g(x) is listed below.

xg(x)
−5−0.2
−41.2
−32.2
−22.8
−13
02.8
12.2
21.2
3−0.2
4−1.9
5−4.1

Table 1

Note that at x=0.2, the graph f takes the value of −4.

Similarly, from the graph f, the values of f(g(x)) is listed below.

xg(x)f(g(x))
−5−0

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