Answer
1) Domain: $[3,\infty)$
2) Range: $[0,\infty )$
Work Step by Step
Given \begin{equation}
f(x)=\sqrt[6]{2 x-6}= \sqrt[6]{2 (x-3)}.
\end{equation} a) This is an even root function because the index, $n=6$, is even. The radicand must be positive. So, we require $$2(x-3)\geq 0\implies x\geq 3.$$ 1) The domain is $[3,\infty)$.
2) The range is $[0,\infty )$.
See graph for proof.
