Question

Помогите пожалуйста
Найти область определения функции

Answer 1

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