Answer :
To determine the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex], we need to consider the expression inside the square root. The square root function is only defined for non-negative values, so that means [tex]\( x - 7 \)[/tex] must be greater than or equal to zero.
Step 1: Set up the inequality
For the square root to be defined, we have:
[tex]\[ x - 7 \geq 0 \][/tex]
Step 2: Solve the inequality
Add 7 to both sides of the inequality to find the values of [tex]\( x \)[/tex]:
[tex]\[ x \geq 7 \][/tex]
Conclusion:
The domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex] is all values of [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex]. Therefore, the correct answer is:
B. [tex]\( x \geq 7 \)[/tex]
Step 1: Set up the inequality
For the square root to be defined, we have:
[tex]\[ x - 7 \geq 0 \][/tex]
Step 2: Solve the inequality
Add 7 to both sides of the inequality to find the values of [tex]\( x \)[/tex]:
[tex]\[ x \geq 7 \][/tex]
Conclusion:
The domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex] is all values of [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex]. Therefore, the correct answer is:
B. [tex]\( x \geq 7 \)[/tex]
