We are asked to find the domain of the function $f(x) = \sqrt{4-x^2}$.

1. Problem Description

We are asked to find the domain of the function $f(x) = \sqrt{4-x^2}$.

2. Solution Steps

The domain of a square root function is the set of all real numbers for which the expression inside the square root is non-negative. Therefore, we must have

$4-x^2 \geq 0$.

We can rearrange this inequality as

$x^2 \leq 4$.

Taking the square root of both sides, we get

$|x| \leq 2$.

This means that $-2 \leq x \leq 2$.

In interval notation, the domain is $[-2, 2]$.

3. Final Answer

The domain of the function is $[-2, 2]$.