Answer
1) Domain: $[-9, \infty)$
2) Range: $[0,\infty )$.
Work Step by Step
Given \begin{equation}
f(x)=\sqrt[6]{x+9}.
\end{equation} a) This is an even root function because the index, $n=6$, is even. The radicand must be positive. So, we require $$x+9\geq 0\implies x\geq -9.$$ 1) The domain is $[-9, \infty)$
2) The range is $[0,\infty )$.
See the graph for proof.
