1 The monotonic increasing interval of the function $f(x)=\log _{\frac{1}{2}}\left(x^{2}-2 x-3\right)$ is $(\quad)$
(A) $(-\infty,-1)$
(B) $(-\infty, 1)$
(C) $(1,+\infty)$
(D) $(3,+\infty)$
Solve: First, find the domain of $f(x)$. From $x^{2}-2 x-3>0$, we get $x<-1$ or $x>3$, so the domain of $f(x)$ is $(-\infty,-1) \cup(3,+\infty)$. And $u=x^{2}-$ $2 x-3=(x-1)^{2}-4$ is monotonically decreasing on $(-\infty,-1)$ and monotonically increasing on $(3,+\infty)$, so, $f(x)=\log _{\frac{1}{2}}\left(x^{2}-2 x-3\right)$ is monotonically increasing on $(-\infty,-1)$ and monotonically decreasing on $(3,+\infty)$, hence the answer is (A).