Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 11: 61

Answer

(a) odd function. (b) odd function. (c) neither odd nor even function. (d) even function.

Work Step by Step

(a) Since we have $f(-t)=\frac{1}{t^4-t+1}-\frac{1}{t^4+t+1}=-f(t)$, then $f $ is an odd function. (b) Since we have $g(-t)=2^{-t}-2^t=-f(t)$, then $f $ is an odd function. (c) Since we have $f(-\theta)=-\sin\theta+\cos\theta\neq f(\theta)\neq -f(\theta)$, then $f $ is neither an odd nor even function. (d) Since we have $H(-\theta)=\sin\theta^2= H(\theta)$, then $H $ is an even function.
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