1. The problem is to find the domain of the function $f(x) = \sqrt{8 - x}$.\n\n2. The domain of a square root function requires the expression inside the root to be non-negative because the square root of a negative number is not a real number.\n\n3. Set the inside of the square root greater than or equal to zero: $$8 - x \geq 0$$\n\n4. Solve the inequality for $x$: $$8 - x \geq 0$$\n$$\Rightarrow -x \geq -8$$\n\n5. When multiplying or dividing an inequality by a negative number, reverse the inequality sign: $$x \leq 8$$\n\n6. Therefore, the domain of $f(x)$ is all real numbers $x$ such that $x \leq 8$. In interval notation, this is $(-\infty, 8]$.