2. The increasing interval of the function $f(x)=\log _{\frac{1}{2}}\left(-x^{2}-2 x+3\right)$ is ( ).
(A) $(-3,-1)$
(B) $[-1,1)$
(C) $(-3,-1]$
(D) $(-1,1)$
2. B.

From $-x^{2}-2 x+3>0$, we get $-3<x<1$.
Therefore, the vertex of the parabola $y=-x^{2}-2 x+3$ is at $(-1,4)$. Thus, the function $y=-x^{2}-2 x+3$ is decreasing in the interval $[-1,1)$.
$$
\begin{array}{l}
\text { Also, } \frac{1}{2}<1, \text { hence, the function } \\
f(x)=\log _{\frac{1}{2}}\left(-x^{2}-2 x+3\right)
\end{array}
$$

is increasing in the interval $[-1,1)$.