Calculus 8th Edition

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

Chapter 1 - Functions and Limits - 1.1 Four Ways to Represent a Function - 1.1 Exercises - Page 22: 70


$f(x)$ is niether an even function nor an odd function. $g(x)$ is an even function.

Work Step by Step

The function $f(x)$ is neither symmetric across the y-axis (even function) nor is it rotationally symmetric (not the same function as before the rotation if you rotate it $180^{o}$ around the origin) so it isn't an odd function either. Therefore the function is an odd function as it doesn't comply with either of the rules for an even or an odd function. The function $g(x)$ is symmetric across the y-axis (symmetric from one side of the y-axis to the other) and therefore complies with the rule for an even function ($f(x)=f(-x)$). Thus, $g(x)$ is an even function.
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