Answer
Domain: $\{x|x\ge4\}$
Work Step by Step
Since functions are defined only over the set of real numbers, the radicand of an even root should be nonnegative. Thus, the radicand of the given function, $f(x)=\sqrt{2x-8},$ should be nonnegative. That is,
\begin{align*}
2x-8\ge0
.\end{align*}
Using the properties of inequality, the solution set of the inequality above is
\begin{align*}\require{cancel}
2x-8+8&\ge0+8
\\
2x&\ge8
\\\\
\dfrac{\cancel2x}{\cancel2}&\ge\dfrac{8}{2}
\\\\
x&\ge4
.\end{align*}
Hence, the domain of $f(x)=\sqrt{2x-8}$ is $\{x|x\ge4\}$.
