Answer :
Let's determine the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex].
For the square root function [tex]\( \sqrt{a} \)[/tex] to be real and defined, the expression inside the square root, [tex]\( a \)[/tex], must be non-negative ([tex]\( a \geq 0 \)[/tex]).
In our function, the expression inside the square root is [tex]\( x - 7 \)[/tex]. Therefore, we set up the following inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
Now, let's solve for [tex]\( x \)[/tex]:
[tex]\[ x - 7 \geq 0 \][/tex]
[tex]\[ x \geq 7 \][/tex]
This means that the domain of the function [tex]\( h(x) \)[/tex] is all [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{D. \quad x \geq 7} \][/tex]
For the square root function [tex]\( \sqrt{a} \)[/tex] to be real and defined, the expression inside the square root, [tex]\( a \)[/tex], must be non-negative ([tex]\( a \geq 0 \)[/tex]).
In our function, the expression inside the square root is [tex]\( x - 7 \)[/tex]. Therefore, we set up the following inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
Now, let's solve for [tex]\( x \)[/tex]:
[tex]\[ x - 7 \geq 0 \][/tex]
[tex]\[ x \geq 7 \][/tex]
This means that the domain of the function [tex]\( h(x) \)[/tex] is all [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{D. \quad x \geq 7} \][/tex]
