Answer
$D(h)=\{x\in \mathbb{R} : x \geq 4\}$
Work Step by Step
The radicand inside a square root should not be negative.
Thus, to find the domain of the given function, we have to solve the inequality
$$3x-12\ge0$$
Solving the inequality above gives:
$$\begin{align*}
3x-12&\ge0\\
3x&\ge12\\
x&\ge\frac{12}{3}\\
x&\ge4
\end{align*}$$
Therefore, the domain of the given function is $\left\{x|x\ge4\right\}$.
