Question

Найдите область определения функции: 1. y=x^2/5x-2 2.y=cosx/корень из x+3 3.y=7+корень из 2x^2-9x

Answer 1

$1)\; \; y=\frac{x^2}{5x-2}\; ,\\\\OOF:\; \; 5x-2\ne 0\; \; \to \; \; 5x\ne 2\; ,\; \; x\ne 0,4\\\\x\in (-\infty ;\, 0,4)\cup (0,4\, ;+\infty )\\\\2)\; \; y=\frac{cosx}{\sqrt{x+3}}\\\\OOF:\; \; \left \{ {{\sqrt{x+3}\ne 0} \atop {x+3\geq 0}} \right. \; \left \{ {{x+3\ne 0} \atop {x+3\geq 0}} \right. \; \Rightarrow \; \; x+30\; ,\; \; x-3\\\\x\in (-3,+\infty )\\\\3)\; \; y=7+\sqrt{2x^2-9x}\\\\OOF:\; \; 2x^2-9x\geq 0\; \; \Rightarrow \; \; x(2x-9)\geq 0\; ,\\\\znaki\; \; x(2x-9):\; \; \; +++[\, 0\, ]---[\, 4,5\, ]+++$

$x\in (-\infty \, ;\, 0\, ]\cup [\, 4,5\; ;\, +\infty )$