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------------------------------------------------ Select the correct answer.

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

A. [tex]$x \leq 5$[/tex]

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

C. [tex]$x \geq 5$[/tex]

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

Answer :

To determine the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex], we need to make sure that the expression inside the square root is non-negative because you cannot take the square root of a negative number in real numbers.

1. Start with the expression inside the square root: [tex]\( x - 7 \)[/tex].

2. Set up the inequality to ensure it's non-negative:
[tex]\[
x - 7 \geq 0
\][/tex]

3. Solve the inequality for [tex]\( x \)[/tex]:
[tex]\[
x \geq 7
\][/tex]

Therefore, the domain of the function [tex]\( h(x) \)[/tex] is all [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].

The correct answer is B. [tex]\( x \geq 7 \)[/tex].

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