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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 find the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex], we need to determine the values of [tex]\( x \)[/tex] for which the function is defined.

1. Focus on the square root part: The expression inside the square root, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero because the square root of a negative number is not defined in the set of real numbers.

2. Set up the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]

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

4. Conclusion: The domain of the function [tex]\( h(x) \)[/tex] is the set of all [tex]\( x \)[/tex] values that satisfy the inequality [tex]\( x \geq 7 \)[/tex].

Therefore, the correct answer is:

C. [tex]\( x \geq 7 \)[/tex]

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