Answer :
To determine the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], we need to focus on the square root part of the function, [tex]\(\sqrt{x - 7}\)[/tex]. The expression inside the square root, [tex]\(x - 7\)[/tex], must be non-negative for the square root to be defined for real numbers.
Here's how you find the domain step-by-step:
1. Set the expression inside the square root greater than or equal to zero:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve the inequality:
[tex]\[
x \geq 7
\][/tex]
This means that [tex]\( x \)[/tex] must be greater than or equal to 7 for the function to be defined.
Therefore, the correct answer is:
B. [tex]\( x \geq 7 \)[/tex]
This tells us that the function can take any real number [tex]\( x \)[/tex] starting from 7 and continuing to infinity.
Here's how you find the domain step-by-step:
1. Set the expression inside the square root greater than or equal to zero:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve the inequality:
[tex]\[
x \geq 7
\][/tex]
This means that [tex]\( x \)[/tex] must be greater than or equal to 7 for the function to be defined.
Therefore, the correct answer is:
B. [tex]\( x \geq 7 \)[/tex]
This tells us that the function can take any real number [tex]\( x \)[/tex] starting from 7 and continuing to infinity.
