Question

помогите пожалуйста ​

Answer 1

Ответ:

$1)\ \ y=\sqrt{\dfrac{2-3x}{x^2-1}}\ \ ,\ \ \ OOF:\ \left\{\begin{array}{l}\dfrac{2-3x}{x^2-1}\geq 0\\x^2-1\ne 0\end{array}\right\ \ \left\{\begin{array}{l}\dfrac{3x-2}{(x-1)(x+1)}\leq 0\\(x-1)(x+1)\ne 0 \end{array}\right\\\\\\\dfrac{3x-2}{(x-1)(x+1)}\leq 0\ \ ,\ \ \ znaki:\ ---(-1)+++\Big[\dfrac{2}{3}\Big]---(1)+++\\\\\\\underline {\ x\in \Big(-\infty ;-1\Big)\cup \Big[\ \dfrac{2}{3}\, ;\, 1\Big)\ }$

$2)\ \ y=\sqrt{\dfrac{x-2}{x^2-9}}\ \ ,\ \ \ OOF:\ \left\{\begin{array}{l}\dfrac{x-2}{x^2-9}\geq 0\\x^2-9\ne 0\end{array}\right\ \ \left\{\begin{array}{l}\dfrac{x-2}{(x-3)(x+3)}\geq 0\\(x-3)(x+3)\ne 0\end{array}\right\\\\\\\dfrac{x-2}{(x-3)(x+3)}\geq 0\ \ ,\ \ znaki:\ ---(-3)+++[\, 2\, ]---(3)+++\\\\\\\underline {\ x\in (-3\, ;\, 2\ ]\cup (\ 3\, ;+\infty \, )\ }$