## Calculus 8th Edition

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