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What is the domain of the function [tex]h[/tex]?



[tex]h(x) = \sqrt{x - 7} + 5[/tex]



A. [tex]x \leq -7[/tex]



B. [tex]x \geq 7[/tex]



C. [tex]x \leq 5[/tex]



D. [tex]x \geq 5[/tex]

Answer :

To find the domain of the function
$$
h(x)=\sqrt{x-7}+5,
$$
we need to ensure that the expression inside the square root is non-negative. This is because the square root of a negative number is not defined in the set of real numbers.

1. Set the expression inside the square root to be greater than or equal to zero:
$$
x - 7 \geq 0.
$$

2. Solve the inequality for $x$:
$$
x \geq 7.
$$

Thus, the domain of the function is all real numbers $x$ such that $x \geq 7$. Comparing with the given options, the correct answer is:

B. $\; x \geq 7$.

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