Calculus (3rd Edition)

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

Chapter 1 - Precalculus Review - Chapter Review Exercises - Page 36: 16


(a) $f(x)$ is even function. (b) $g(x)$ is neither even nor odd. (c) $f(x)$ is even.

Work Step by Step

(a) $f(x)=x^4-3x^2$, since $$f(-x)=(-x)^4-3(-x)^2=x^4-3x^2=f(x)$$ then $f(x)$ is an even function. (b) $g(x)=\sin(x+1)$, since $g(-x)=\sin(-x+1)\neq g(x)$ and $g(-x)\neq -g(x)$, then $g(x)$ is neither even nor odd. (c) since $f(-x)=2^{-(-x)^2}=2^{-x^2}=f(x)$ then $f(x)$ is even.
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