Answer :
To determine the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], we need to ensure that the expression inside the square root is non-negative. This is because the square root of a negative number is not defined in the set of real numbers.
Step-by-step solution:
1. Identify the constraint for the square root:
The function has a square root, [tex]\( \sqrt{x - 7} \)[/tex]. For this to be defined, the expression inside the square root, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero.
2. Set up the inequality:
[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]
So, 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-by-step solution:
1. Identify the constraint for the square root:
The function has a square root, [tex]\( \sqrt{x - 7} \)[/tex]. For this to be defined, the expression inside the square root, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero.
2. Set up the inequality:
[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]
So, 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].
