Answer
Domain: $x\geq \frac{7}{2}$
Range: $y\geq 0$
Work Step by Step
Given \begin{equation}
g(x)=\sqrt{2 x-7}.
\end{equation} The radicand of a radical function must be positive. This means that we must have $$2x-7\geq 0\implies x\geq \frac{7}{2}.$$ Also, we see that the function's value must satisfy $y\geq 0$ because $\sqrt{2x-7}\geq 0$.
We got: \begin{equation}
\begin{aligned}
\textbf{Domain :}\quad & x\geq \frac{7}{2}\\
\textbf{Range :}\quad & y\geq 0\\\\
\end{aligned}
\end{equation}
