# Question #0dd78

##### 1 Answer
Jan 8, 2018

$g \left(x\right)$ is an even function.

#### Explanation:

If $g \left(- x\right) = g \left(x\right)$, the function is even, and if $g \left(- x\right) = - g \left(x\right)$, it is odd.

To find out which one it is, we plug in $- x$:
$g \left(- x\right) = {\left(- x\right)}^{2} + {\cos}^{2} \left(- x\right)$

Cosine is an even function, and a negative squared is positive, so the minus signs just disappear:
$g \left(- x\right) = {x}^{2} + {\cos}^{2} \left(x\right) = g \left(x\right)$

Since $g \left(- x\right) = g \left(x\right)$, we can conclude that $g \left(x\right)$ is an even function.