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

Answer

No.

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.