College

Select the correct answer.

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

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

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

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

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

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

Answer :

To determine the domain of the function
[tex]$$
h(x) = \sqrt{x-7} + 5,
$$[/tex]
we first need to ensure that the expression under 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.

The expression under the square root is [tex]$x-7$[/tex], so we need to have:
[tex]$$
x - 7 \geq 0.
$$[/tex]

Now, solve this inequality:
[tex]\[
x \geq 7.
\][/tex]

This means that the function [tex]$h(x)$[/tex] is defined for all real numbers [tex]$x$[/tex] that are greater than or equal to [tex]$7$[/tex].

Thus, the domain of the function is:
[tex]$$
\{ x \in \mathbb{R} : x \geq 7 \}.
$$[/tex]

So, the correct choice is:

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