1. The monotonic increasing interval of the function $f(x)=\log _{\frac{1}{2}}\left(x^{2}-2 x-3\right)$ is
A. $(-\infty,-1)$
B. $(-\infty, 1)$
C. $(1,+\infty)$
D. $(3,+\infty)$
Solve:
$y=x^{2}-2 x-3=(x+1)(x-3)>0 \Rightarrow x \in(-\infty,-1) \bigcup(3,+\infty)$, by the monotonicity of composite functions, the increasing interval of the function $f(x)=\log _{\frac{1}{2}}\left(x^{2}-2 x-3\right)$ is $(-\infty,-1)$. Therefore, the answer is $A$.