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Answer :
We want to find the domain of the function
$$h(x) = \sqrt{x - 7} + 5.$$
Since the square root function is only defined when its argument is non-negative, we require that the expression inside the square root is at least 0. That is, we need:
$$x - 7 \geq 0.$$
Adding 7 to both sides, we obtain:
$$x \geq 7.$$
Thus, the domain of $h(x)$ is all real numbers $x$ such that $x \geq 7$.
Therefore, the correct answer is:
$$\textbf{D. } x \geq 7.$$
$$h(x) = \sqrt{x - 7} + 5.$$
Since the square root function is only defined when its argument is non-negative, we require that the expression inside the square root is at least 0. That is, we need:
$$x - 7 \geq 0.$$
Adding 7 to both sides, we obtain:
$$x \geq 7.$$
Thus, the domain of $h(x)$ is all real numbers $x$ such that $x \geq 7$.
Therefore, the correct answer is:
$$\textbf{D. } x \geq 7.$$
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