Question

is $x^{40}$ an even or odd function?
even function
odd function
is $cos^{2}(x)$ an even or odd function?
even function
odd function

Explanation:

Step1: Define even function test

A function $f(x)$ is even if $f(-x)=f(x)$.

Step2: Test $f(x)=x^{40}$

$f(-x)=(-x)^{40}=x^{40}=f(x)$

Step3: Test $g(x)=\cos^2(x)$

First, $\cos(-x)=\cos(x)$ (cosine is even). Then $g(-x)=\cos^2(-x)=(\cos(x))^2=\cos^2(x)=g(x)$

Answer:

1. even function
2. even function