1. The problem involves understanding the domain of the function $f(x) = \sqrt{4 - x}$. 2. The square root function requires the radicand (expression inside the root) to be non-negative for real values, so we set: $$4 - x \geq 0$$ 3. Solve the inequality: $$4 \geq x$$ or equivalently $$x \leq 4$$ 4. Therefore, the domain of $f(x)$ is all real numbers $x$ such that $x$ is less than or equal to 4. 5. In interval notation, this domain is: $$]-\infty, 4]$$ 6. Among the given options, the correct domain matches the interval $]-\infty, 4]$ or any union that includes this interval without excluding the endpoint 4. Final answer: The domain of $f(x) = \sqrt{4 - x}$ is $]-\infty, 4]$.