1. Let $a$ be a real number. If for any real number $x$, the inequality $x^{2} \log _{\frac{1}{2}}\left(a^{2}-2 a-3\right)-2 x+1 \geqslant 0$ always holds, then the range of values for $a$ is $\qquad$
\[
\begin{array}{l}
0.1 .1-\frac{3 \sqrt{2}}{2} \leqslant a0, \\
\log _{\frac{1}{2}}\left(a^{2}-2 a-3\right)>0, \\
\Delta=4-4 \log _{\frac{1}{2}}\left(a^{2}-2 a-3\right) \leqslant 0
\end{array}
\]
\[
\Leftrightarrow\left\{\begin{array}{l}
0 \text{I} \text{ when } 2<a-1 \leqslant \frac{3}{\sqrt{2}}, \text{ i.e., } 3<a \leqslant 1+\frac{3}{\sqrt{2}}; \\
\text{when } a<1, 2<1-a \leqslant \frac{3}{\sqrt{2}}, \text{ i.e., } 1-\frac{3}{\sqrt{2}} \leqslant a<-1.
\end{array}\right.
\]