2. (2002 National High School Competition Question) 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. $(3,+\infty)$
2. A. Reason: From $x^{2}-2 x-3>0$ we have $x3$, thus the domain of the function $\log _{\frac{1}{2}}\left(x^{2}-2 x-3\right)$ is $x3$. The quadratic function $u=x^{2}-2 x-3$ is monotonically decreasing in $(-\infty,-1)$ and monotonically increasing in $(3,+\infty)$, while $\log \frac{1}{2} u$ is monotonically decreasing in $(0$, $+\infty)$. Therefore, $\log _{\frac{1}{2}}\left(x^{2}-2 x-3\right)$ is monotonically increasing in $(-\infty,-1)$.