Question

Помогите пожалуйста
Найти область определения функции

Answer 1

$y=\sqrt{(5+x)(8-4x)} \\\\\\\boxed{\sqrt{f(x)}\Rightarrow f(x)\geq 0}\\\\(5+x)(8-4x)\geq 0\\\\\left \{ \begin{array}{l} 5+x\geq 0\\ 8-4x\geq 0 \\5+x\leq 0 \\ 8-4x\leq 0\end{array} \Rightarrow \; \left \{ \begin{array}{l} x\geq -5\\ x\leq 2 \\x\leq -5 \\ x\geq 2\end{array} \Rightarrow\left \{ \begin{array}{l} x \in [-5;\;2] \\ x \in \varnothing \end{array} \Rightarrow \; x\in [-5;\;2].$