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

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

Answer :

To determine the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], we need to analyze when the expression inside the square root is defined.

1. The square root function is only defined for non-negative numbers. This means the expression under the square root, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero:
[tex]\[
x - 7 \geq 0
\][/tex]

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

This tells us that [tex]\( x \)[/tex] must be greater than or equal to 7 for the function [tex]\( h(x) \)[/tex] to be defined.

Thus, the domain of the function [tex]\( h \)[/tex] is [tex]\( x \geq 7 \)[/tex].

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

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