Question

Найдите значение x при котором выражение имеет смысл.

Answer 1

$1)\ \ \dfrac{x-2}{\sqrt{x} }\ \ ,\ \ \ OOF:\ x\geq \ i\ \ x\ne 0\0\ \ \to \ \ \underline {\ x\in (\ 0\, ;+\infty )\ }\\\\\\2)\ \ \dfrac{x}{\sqrt{-x}}\ \ ,\ \ \ OOF:\ -x>0\ \ ,\ \ x<0\ \ \to \ \ \underline {\ x\in (-\infty \, ;\, 0\ )\ }$

$3)\ \ \dfrac{3}{\sqrt{x}-3}\ \ ,\ \ \ OOF:\ \left\{\begin{array}{l}\sqrt{x}-3\ne 0\\x\geq 0\end{array}\right\ \ \left\{\begin{array}{ccc}\sqrt{x}\ne 3\\x\geq 3\end{array}\right\ \ \left\{\begin{array}{ccc}x\ne 9\\x\geq 0\end{array}\right\to \\\\\\{}\ \ \ \ \ \underline {\ x\in [\ 0\, ;\, 9)\cup (\, 9;+\infty )}\\\\\\4)\ \ \sqrt{-x^2}\ \ ,\ \ OOF:\ \ -x^2\geq 0\ \ \to \ \ x^2\leq 0\ \ \to \ \ \ \underline {\ x\in \varnothing \ }$