Answer :
To determine the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], we need to analyze when the expression inside the square root is defined.
1. The square root function is only defined for non-negative numbers. This means the expression under the square root, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve the inequality:
[tex]\[
x \geq 7
\][/tex]
This tells us that [tex]\( x \)[/tex] must be greater than or equal to 7 for the function [tex]\( h(x) \)[/tex] to be defined.
Thus, the domain of the function [tex]\( h \)[/tex] is [tex]\( x \geq 7 \)[/tex].
The correct answer is:
C. [tex]\( x \geq 7 \)[/tex]
1. The square root function is only defined for non-negative numbers. This means the expression under the square root, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve the inequality:
[tex]\[
x \geq 7
\][/tex]
This tells us that [tex]\( x \)[/tex] must be greater than or equal to 7 for the function [tex]\( h(x) \)[/tex] to be defined.
Thus, the domain of the function [tex]\( h \)[/tex] is [tex]\( x \geq 7 \)[/tex].
The correct answer is:
C. [tex]\( x \geq 7 \)[/tex]
