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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 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 ensure that the expression under the square root is non-negative. This is important because the square root of a negative number is not defined within the set of real numbers.

Here's how we can find the domain step-by-step:

1. Identify the expression under the square root:
The expression is [tex]\( x - 7 \)[/tex].

2. Set up the inequality for the domain:
To keep the expression under the square root non-negative, we need:
[tex]\[
x - 7 \geq 0
\][/tex]

3. Solve the inequality:
Add 7 to both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x \geq 7
\][/tex]

4. Conclusion about the domain:
Therefore, the domain of the function is all [tex]\( x \)[/tex] values such that [tex]\( x \geq 7 \)[/tex].

So, the correct answer is B. [tex]\( m \geq 7 \)[/tex].

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