The problem asks us to determine if the function $f(x) = \cos(x)$ is even or odd. We need to evaluate $f(-x)$.

1. Problem Description

The problem asks us to determine if the function $f(x) = \cos(x)$ is even or odd. We need to evaluate $f(-x)$.

2. Solution Steps

To determine if a function is even or odd, we need to examine $f(-x)$.

If $f(-x) = f(x)$, the function is even.

If $f(-x) = -f(x)$, the function is odd.

If neither of these is true, the function is neither even nor odd.

Given $f(x) = \cos(x)$, we need to find $f(-x)$.

$f(-x) = \cos(-x)$

Since the cosine function is an even function, we know that $\cos(-x) = \cos(x)$.

Therefore, $f(-x) = \cos(-x) = \cos(x) = f(x)$.

Since $f(-x) = f(x)$, the function $f(x) = \cos(x)$ is an even function.

3. Final Answer

$f(-x) = \cos(x)$, thus $f(x)$ is an even function.