Question

Find the domain of definition of the following function.
$f\left(x\right),=\sqrt{2-x}+\sqrt{1+x}.$

Answer 1

$f\left(x\right)=\sqrt{2-x}+\sqrt{1+x}$

$2-x\ge 0$

$1+x\ge 0$

$2-x\ge 0$

$x\le 2$

$1+x\ge 0$

$x\ge -1$

So the domain is $[-1,2]$.