Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 45: 66



Work Step by Step

When $f$ is odd, we can find that: $f(g(-x)) = f(-g(x))= -f(g(x)) = -h(x)$ Therefore $h$ is odd. However, when $f$ is even, we can find that: $f(g(-x)) = f(-g(x))= f(g(x)) = h(x)$ Therefore $h$ is even. Thus, $h$ is not always an odd function.
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