Найдите область определения функции

Question 1

Question 2

Решите задачу:

$y=\sqrt{(x^2-1)\cdot log_{\frac{1}{3}}(3-x)}\\\\OOF:\; \; (x^2-1)\cdot log_{\frac{1}{3}}(3-x) \geq 0\; \; \Rightarrow \\\\ \left \{ {{x^2-1 \geq 0} \atop {log_{\frac{1}{3}}(3-x) \geq 0\; ,\; 3-x\ \textgreater \ 0}} \right. \; \; ili\; \; \left \{ {{x^2-1 \leq 0} \atop {log_{ \frac{1}{3}}(3-x) \leq 0,\; 3-x\ \textgreater \ 0}} \right. \\\\1)\; \; a)\; \; x^2-1 \geq 0\quad \to \quad (x-1)(x+1) \geq 0\\\\+++[-1\, ]---[\, 1\, ]+++\\\\x\in (-\infty ,-1\; ]\cup [\, 1,+\infty )$

$b)\; \; 3-x\ \textgreater \ 0\; \; \Rightarrow \; \; \; x\ \textless \ 3\; ,\; \; x\in (-\infty ,3)$

$c)\; \; log_{\frac{1}{3}}(3-x) \geq 0\\\\log_{\frac{1}{3}}(3-x) \geq log_{\frac{1}{3}}1\; \; \Rightarrow \; \; \; 3-x \leq 1\; ,\; \; \; x \geq 2\\\\d)\; \; \left \{ {{x\in (-\infty ,-1\, ]\cup [\, 1,+\infty )} \atop {x\in (-\infty ,3)\; ,\; \; x\in [\, 2,+\infty )}} \right. \; \; \Rightarrow \; \; \; x\in [\; 2,3)$

$2)\; \; a)\; \; x^2-1 \leq 0\; \; \to \; \; \; (x-1)(x+1) \leq 0\\\\x\in [-1,1\; ]\\\\b)\; \; 3-x\ \textgreater \ 0\; \; \; \to \; \; \; x\ \textless \ 3\\\\c)\; \; log_{\frac{1}{3}}(3-x) \leq 0\\\\3-x \geq 1\; \; \; \to \; \; \; x \leq 2\\\\d)\; \; \left \{ {{x\in [-1,\; 1\; ]} \atop {x\in (-\infty ,3)\; ,\; x\in (-\infty ,2\; ]}} \right. \; \; \Rightarrow \; \; \; x\in [-1,1\; ]\\\\Otvet:\; \; x\in [-1,1\; ]\cup [\; 2,3)\; .$