We need to find the domain of the function $f(x) = \sqrt{4-x^2}$. The domain is the set of all possible values of $x$ for which the function is defined.

1. Problem Description

We need to find the domain of the function $f(x) = \sqrt{4-x^2}$. The domain is the set of all possible values of $x$ for which the function is defined.

2. Solution Steps

The function $f(x) = \sqrt{4-x^2}$ is defined only when the expression inside the square root is non-negative. Therefore, we must have

$4-x^2 \ge 0$.

$4 \ge x^2$.

$x^2 \le 4$.

Taking the square root of both sides, we get

$|x| \le 2$.

This means $-2 \le x \le 2$.

So, the domain is the interval $[-2, 2]$.

3. Final Answer

The domain of the function $f(x) = \sqrt{4-x^2}$ is $[-2, 2]$.