1. The function $f(x)=-\log _{\frac{1}{2}}\left(x^{2}-a x-a\right)$ is decreasing on the interval $(-\infty, 1-\sqrt{3})$, the range of values for $a$ is $\qquad$ .
1. $2(1-\sqrt{3}) \leqslant a \leqslant 2$.
$f(x)=\log _{2}\left(x^{2}-a x-a\right)$. Let $t=x^{2}-a x-a$, by the problem, $t$ is decreasing on $(-\infty, 1-\sqrt{3})$, then $\frac{a}{2} \geqslant 1-\sqrt{3}$, i.e., $a \geqslant 2(1-\sqrt{3})$. Also, when $x \in(-\infty, 1-\sqrt{3})$, $t>0$ must hold, which only requires that $t \geqslant 0$ when $x=1-\sqrt{3}$, then $(1-\sqrt{3})^{2}-a(1-\sqrt{3})-a \geqslant 0$, yielding $a \leqslant 2$. Therefore, $2(1-\sqrt{3}) \leqslant a \leqslant 2$.