Answer :
To determine the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex], you need to focus on the expression inside the square root, which is [tex]\( x-7 \)[/tex]. The square root function is only defined for non-negative numbers, which means the expression inside the square root must be greater than or equal to zero.
Here’s how you can find the domain:
1. Set up the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
Add 7 to both sides of the inequality:
[tex]\[
x \geq 7
\][/tex]
3. Interpret the solution:
This tells us that [tex]\( x \)[/tex] must be greater than or equal to 7 for the function to be defined.
Thus, the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex] is [tex]\( x \geq 7 \)[/tex].
The correct answer is:
C. [tex]\( x \geq 7 \)[/tex]
Here’s how you can find the domain:
1. Set up the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
Add 7 to both sides of the inequality:
[tex]\[
x \geq 7
\][/tex]
3. Interpret the solution:
This tells us that [tex]\( x \)[/tex] must be greater than or equal to 7 for the function to be defined.
Thus, the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex] is [tex]\( x \geq 7 \)[/tex].
The correct answer is:
C. [tex]\( x \geq 7 \)[/tex]
