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) $(3,+\infty)$
-1. (A).
From $x^{2}-2 x-3>0$ we have $x<-1$ or $x>3$, so the domain of the function $\log _{\frac{1}{2}}\left(x^{2}-2 x-3\right)$ is $x<-1$ or $x>3$. The quadratic function $u=x^{2}-2 x-3$ is monotonically decreasing in $(-\infty,-1)$ and monotonically increasing in $(3,+\infty)$. Since $\log _{\frac{1}{2}} u$ is monotonically decreasing in $(0,+\infty)$, $\log _{\frac{1}{2}}\left(x^{2}-2 x-3\right)$ is monotonically increasing in $(-\infty,-1)$.