Example 3 (1) Find the domain of the function $y=\sqrt{\frac{1}{2}-\log _{2}(3-x)}$;
(2) Given that the domain of $f(x)$ is $[0,1]$, find the domain of the function $y=f\left(\log _{\frac{1}{2}}(3-x)\right)$.
(1) $\left\{\begin{array}{l}\frac{1}{2}-\log _{2}(3-x) \geqslant 0, \\ 3-x>0\end{array} \Rightarrow 0<3-x \leqslant \sqrt{2}\right.$, so the domain is $[3-\sqrt{2}, 3)$.
(2) Since the domain of $f(x)$ is $[0,1]$, to make $y=f\left(\log _{\frac{1}{2}}(3-x)\right)$ meaningful, it must satisfy $0 \leqslant \log _{\frac{1}{2}}(3-x) \leqslant 1 \Rightarrow \log _{\frac{1}{2}} 1 \leqslant \log _{\frac{1}{2}}(3-x) \leqslant \log _{\frac{1}{2}} \frac{1}{2} \Rightarrow \frac{1}{2} \leqslant 3-x \leqslant 1$, so the domain is $\left[2, \frac{5}{2}\right]$.