Question

Найдите область определения

Answer 1

$f(x)=\sqrt{x-\frac{8}{x-2}}\\\\OOF:\; \; x-\frac{8}{x-2}\geq 0\; ,\; \; \frac{x\cdot (x-2)-8}{x-2}\geq 0\; ,\; \; \frac{x^2-2x-8}{x-2}\geq 0\; ,\\\\x^2-2x-8=0\; \; \to \; \; x_1=-2\; ,\; x_2=4\; \; (teorema\; Vieta)\\\\\frac{(x-4)(x+2)}{x-2}\geq 0\; ,\; \; x\ne 2\\\\znaki:\; \; ---[-2\, ]+++(2)---[\, 4\, ]+++\\\\x\in [-2,2)\cup [\, 4,+\infty )$