BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.3, Problem 52E
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.

Expert Solution

Explanation of Solution

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))
−5−0.2−4
−41.2−3.3
−32.2−1.7
−22.8−0.5
−13−0.2
02.8−0.5
12.2−1.7
21.2−3.3
3−0.2−4
4−1.9−2.2
5−4.11.9

Table 2

Use Table 2 to sketch the graph of fg.

Let x be represented in x-axis and f(g(x)) be represented in y-axis. The graph of fg is shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.3, Problem 52E

From Figure1, it is observed that the graph of f(g(x)) intersects the x-axis exactly at point.

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