I. Multiple Choice (This question is worth 36 points, 6 points per sub-question)
1. The interval of monotonic increase for 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) $(3,+\infty)$
(A)
I. Multiple Choice
1.【Analysis and Solution】From $x^{2}-2 x-3=(x+1)(x-3)>0$ we have $x3$, so the domain of the function $\log _{\frac{1}{2}}\left(x^{2}-\right.$ $2 x-3)$ is $x3$. Also, because $u=x^{2}-2 x-3$ is monotonically decreasing in $(-\infty,-1)$ and monotonically increasing in $(3,+\infty)$. And $\log _{\frac{1}{2}} u$ is monotonically decreasing in $(0,+\infty)$, thus $\log _{\frac{1}{2}}\left(x^{2}-2 x-3\right)$ is monotonically increasing in $(-\infty,-1)$, hence the answer is A.