Answer
Domain:$[-2,2]$
Range:$ [0,4]$
Work Step by Step
The square root restricts the domain to x for which the radicand is nonnegative,
$16-x^{4} \geq 0$
$x^{4} \leq 16$
$|x| \leq \sqrt[4]{16}$
$|x| \leq 2$.
Domain:$[-2,2]$
Range: $y \geq 0$
and y is maximum when $x^{4}$ is minimal (0),
$y \leq \sqrt{16}$
$0 \leq y \leq 4$.
Range:$ [0,4]$
