Answer :
To determine the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], we need to make sure that the expression inside the square root is non-negative, because the square root of a negative number is not a real number.
1. Consider the expression inside the square root: [tex]\( x - 7 \)[/tex].
2. To ensure the expression is non-negative, set up the inequality: [tex]\( x - 7 \geq 0 \)[/tex].
3. Solve for [tex]\( x \)[/tex]:
[tex]\[ x - 7 \geq 0 \][/tex]
[tex]\[ x \geq 7 \][/tex]
Therefore, the domain of the function [tex]\( h(x) \)[/tex] is all values of [tex]\( x \)[/tex] that are greater than or equal to 7.
So, the correct answer is:
[tex]\[ \boxed{x \geq 7} \][/tex]
This corresponds to option C:
[tex]\[ \boxed{C. \; x \geq 7} \][/tex]
1. Consider the expression inside the square root: [tex]\( x - 7 \)[/tex].
2. To ensure the expression is non-negative, set up the inequality: [tex]\( x - 7 \geq 0 \)[/tex].
3. Solve for [tex]\( x \)[/tex]:
[tex]\[ x - 7 \geq 0 \][/tex]
[tex]\[ x \geq 7 \][/tex]
Therefore, the domain of the function [tex]\( h(x) \)[/tex] is all values of [tex]\( x \)[/tex] that are greater than or equal to 7.
So, the correct answer is:
[tex]\[ \boxed{x \geq 7} \][/tex]
This corresponds to option C:
[tex]\[ \boxed{C. \; x \geq 7} \][/tex]
