Question

найти область значений функции

Answer 1

Ответ:

Объяснение:

                       Знайти область визначення функції.

$\displaystyle\\1)\ y=\sqrt{4-|x|} +\frac{1}{x+2} \\\\\left \{ {{4-|x|\geq 0} \atop {x+2\neq 0}} \right. \ \ \ \ \left \{ {{4\geq |x|} \atop {x\neq -2}} \right. \ \ \ \ \left \{ {{|x|\leq 4} \atop {x\neq -2}} \right. \ \ \ \ \left\{\begin{array}{ccc}x\leq 4\\-x\leq 4\ |*(-1)\\x\neq -2\end{array}\right\ \ \ \ \left\{\begin{array}{ccc}x\leq 4\\x\geq -4\\x\neq-2 \end{array}\right\\\\\\\Rightarrow\ \ \ \ \ x\in[-4;-2)U(-2;4].$

$\displaystyle\\2)\ y=\sqrt{|x|-3}+\frac{1}{\sqrt{x+1} } \\\\\left \{ {{|x|-3\geq 0} \atop {x+1 > 0}} \right. \ \ \ \ \left \{ {{|x|\geq 3} \atop {x > -1}} \right. \ \ \ \ \left\{\begin{array}{ccc}x\geq 3\\-x\geq 3\ |*(-1)\\x > -1\end{array}\right \ \ \ \ \left\{\begin{array}{ccc}x\geq 3\\x\leq -3\\x > -1\end{array}\right\ \ \ \ \ \ \Rightarrow\\\\x\in[3;+\infty).$

$\displaystyle\\3)\ y=\sqrt{|x+1|(x-3)} \\\\|x+1|(x-3)\geq 0\\\\|x+1|\geq 0\ \ \ \ \Rightarrow\ \ \ \ \\\\x-3\geq 0\\\\x\geq 3\ \ \ \ \Rightarrow\\\\x\in[3;+\infty).$