Answer
1) Domain: $[0,\infty)$
2) Range: $(-\infty,0]$
Work Step by Step
Given \begin{equation}
f(x)=-\frac{2}{3} \sqrt[8]{x}.
\end{equation} a) This is an even root function because the index, $n=8$, is even. Both the domain and range are given by:
1) The domain is $[0,\infty)$.
2) The range is $(-\infty,0]$.
See the graph for proof.
