Example 2 Find the monotonic intervals of $f(x)=\log _{\frac{1}{2}}\left(3-2 x-x^{2}\right)$.
The function $\mu=3-2 x-x^{2}$ is increasing on $(-\infty,-1)$ and decreasing on $(-1,+\infty)$, while the function $f(x)=\log _{\frac{1}{2}}\left(3-2 x-x^{2}\right)$ has a domain of $(-3,1)$. Therefore, the function $f(x)=$ $\log _{\frac{1}{2}}\left(3-2 x-x^{2}\right)$ is decreasing on $(-3,-1)$ and increasing on $(-1,1)$.

Key Points for Solving the Problem When studying the properties of a function, one should first determine its domain. Here, when studying the monotonicity of a logarithmic function, it should be done within its domain to be meaningful.