College

Select the correct answer.

What is the domain of the function [tex]h(x) = \sqrt{x-7} + 5[/tex]?

A. [tex]x \geq 5[/tex]
B. [tex]x \geq 7[/tex]
C. [tex]x \leq -7[/tex]
D. [tex]x \leq 5[/tex]

Answer :

To find the domain of the function
[tex]$$
h(x) = \sqrt{x - 7} + 5,
$$[/tex]
we must ensure that the expression inside the square root is non-negative. This is because the square root function is only defined for non-negative values in the set of real numbers.

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

2. Solve the inequality for [tex]$x$[/tex]:
[tex]$$
x \geq 7.
$$[/tex]

Therefore, the domain of the function is all real numbers [tex]$x$[/tex] such that [tex]$x \geq 7$[/tex].

The correct answer is:

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