Answer
1) Domain: $[-2, \infty)$
2) Range: $[0,\infty )$
Work Step by Step
Given
\begin{equation}
h(x)=\sqrt[4]{x+2}.
\end{equation} a) This is an even root function because the index, $n=4$, is even. The radicand must be positive. So, we require $$x+2\geq 0\implies x\geq -2.$$ 1) The domain is $[-2, \infty)$.
2) The range is $[0,\infty )$.
See the graph for proof.
