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 10: 60


a) odd b) neither odd nor even c) even

Work Step by Step

a) $f(x)= x^{5}$ $f(-x)= (-x)^{5}=-x^{5}= -f(x)$. A function is odd when $f(-x)=-f(x)$ for all x. Therefore, this is an odd function. b) $g(t)= t^{3}-t^{2}$ $g(-t)= (-t)^{3}-(-t)^{2}= -t^{3}-t^{2}\ne g(t)$ Also, $g(-t)\ne -g(t)$. Therefore, this function is neither odd nor even. c) $F(t)=\frac{1}{t^{4}+t^{2}}$ $F(-t)= \frac{1}{(-t)^{4}+(-t)^{2}}=\frac{1}{t^{4}+t^{2}}= F(t)$ F is even as F(-t)=F(t).
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