Question

Find domain and range of the real function $f\left(x\right)=\sqrt{9-x^2}$.

Answer 1

$f\left(x\right)=\sqrt{9-x^2}$
$f\left(x\right)$ is defined for $9-x^2\ge 0$
$\Rightarrow x^2\le 9=3^2$
$\Rightarrow -3\le x\le 3$
$\therefore$ Domain of $f=[-3,3]$
Range of $f=[0,3]$