Question

Найдите область опрелеления функции:
$\sqrt{ \frac{4x - 8}{x {}^{2} + 2x - 15} }$

Answer 1

$\LARGE \\ \sqrt{4x-8\over x^2+2x-15}\\ {4x-8\over x^2+2x-15}\geq 0\\ {4(x-2)\over x^2+2x-15}\geq 0\\ x^2+2x-15=0\\ \left\{\begin{matrix} x_1+x_2=-2\\ x_1\cdot x_2=-15 \end{matrix}\right.\; \; x_1=-5, x_2=3\\ {x-2\over(x+5)(x-3)}\geq 0\\\\ -----\; \boldsymbol{-5}\;+++++\;\boldsymbol{2}\;-----\; \boldsymbol{3} \;+++++\\ x\in (-5;2]\cup (3;+\infty)$