Question

The domain of the function$\sqrt{x^2-5x+6}+\sqrt{2x+8-x^2}$is

Answer 1

$\begin{array}{c}f\left(x\right)=\sqrt{x^2-5x+6}+\sqrt{2x+8-x^2}\\ Domainoff\left(x\right)=x^2-5x+\ge 0\&2x+8-x^2\ge 0\\ =\left(x-2\right)\left(x-3\right)\ge 0\&x^2-2x-8\le 0\\ x\in (-\infty ,2]\cup [3,\infty )\&\left(x-4\right)\left(x+2\right)\le 0\\ x\in (-\infty ,2]\cup [3,\infty )\&x\in \left[-2,4\right]\\ \Rightarrow \left\{-2\right\}\cup \left[3,4\right]\end{array}$