9.021. $y=\sqrt{-\frac{\log _{0.3}(x-1)}{\sqrt{-x^{2}+2 x+8}}}$.

9.021. $y=\sqrt{-\frac{\log _{0.3}(x-1)}{\sqrt{-x^{2}+2 x+8}}}$.
## Solution.

$$
\begin{aligned}
& -\frac{\log _{0.3}(x-1)}{\sqrt{-x^{2}+2 x+8}} \geq 0, \frac{\log _{0.3}(x-1)}{\sqrt{-x^{2}+2 x+8}} \leq 0,\left\{\begin{array}{l}
\log _{0.3}(x-1) \leq 0, \\
-x^{2}+2 x+8>0
\end{array} \Leftrightarrow\right. \\
& \Leftrightarrow\left\{\begin{array} { l } 
{ x - 1 \geq 1 , } \\
{ x ^ { 2 } - 2 x - 8 < 0 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
x \geq 2, \\
-2 \leq x<4
\end{array} \Leftrightarrow 2 \leq x<4 .\right.\right.
\end{aligned}
$$

Answer: $\quad x \in[2 ; 4)$.

Solve the inequalities (9.022-9.095):
