Answer :
To determine the domain of the function [tex]\(h(x) = \sqrt{x-7} + 5\)[/tex], we need to focus on the part of the function under the square root, [tex]\(\sqrt{x-7}\)[/tex].
Square roots are only defined for non-negative values, which means the expression inside the square root must be greater than or equal to zero. This gives us the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
To solve this inequality, we simply add 7 to both sides:
[tex]\[ x \geq 7 \][/tex]
This means that for the function [tex]\(h(x)\)[/tex] to be valid, [tex]\(x\)[/tex] must be at least 7 or greater. Therefore, the domain of the function [tex]\(h(x) = \sqrt{x-7} + 5\)[/tex] is all [tex]\(x\)[/tex] such that [tex]\(x \geq 7\)[/tex].
The correct answer is:
D. [tex]\( x \geq 7 \)[/tex]
Square roots are only defined for non-negative values, which means the expression inside the square root must be greater than or equal to zero. This gives us the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
To solve this inequality, we simply add 7 to both sides:
[tex]\[ x \geq 7 \][/tex]
This means that for the function [tex]\(h(x)\)[/tex] to be valid, [tex]\(x\)[/tex] must be at least 7 or greater. Therefore, the domain of the function [tex]\(h(x) = \sqrt{x-7} + 5\)[/tex] is all [tex]\(x\)[/tex] such that [tex]\(x \geq 7\)[/tex].
The correct answer is:
D. [tex]\( x \geq 7 \)[/tex]
