Question

Знайдіть область визначення функції:
$f(x) = \sqrt{x^{2} - 5x } - \frac{3}{\sqrt{-x-1} }$

Answer 1

$\displaystyle\bf\\f(x)=\sqrt{x^{2} -5x} -\frac{3}{\sqrt{-x-1} } \\\\\\\left \{ {{x^{2} -5x\geq 0} \atop {-x-1>0}} \right. \\\\\\\left \{ {{x(x-5)\geq 0} \atop {-x>1}} \right.\\\\\\\left \{ {{x\in\Big(-\infty \ ; \ 0\Big] \ \cup \ \Big[5 \ ; \ +\infty\Big)} \atop {x<-1}} \right. \\\\\\Otvet:x\in\Big(-\infty \ ; \ -1\Big)$