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, as square roots must have non-negative values to be defined in the set of real numbers.
1. Start with the expression inside the square root: [tex]\( x - 7 \)[/tex].
2. To ensure the square root is defined, the expression must be greater than or equal to zero:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve this inequality to find the values of [tex]\( x \)[/tex] for which the function is defined:
[tex]\[
x \geq 7
\][/tex]
This means the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex] is defined for all [tex]\( x \)[/tex] that are greater than or equal to 7. Therefore, the domain of the function [tex]\( h \)[/tex] is:
B. [tex]\( x \geq 7 \)[/tex]
This is the correct choice for the domain of the function [tex]\( h(x) \)[/tex].
1. Start with the expression inside the square root: [tex]\( x - 7 \)[/tex].
2. To ensure the square root is defined, the expression must be greater than or equal to zero:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve this inequality to find the values of [tex]\( x \)[/tex] for which the function is defined:
[tex]\[
x \geq 7
\][/tex]
This means the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex] is defined for all [tex]\( x \)[/tex] that are greater than or equal to 7. Therefore, the domain of the function [tex]\( h \)[/tex] is:
B. [tex]\( x \geq 7 \)[/tex]
This is the correct choice for the domain of the function [tex]\( h(x) \)[/tex].
