Answer :
To determine the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], we need to focus on the expression inside the square root.
The expression [tex]\( \sqrt{x - 7} \)[/tex] is only defined when the value inside the square root is non-negative. This means that:
[tex]\[ x - 7 \geq 0 \][/tex]
To solve this inequality for [tex]\( x \)[/tex], we add 7 to both sides:
[tex]\[ x \geq 7 \][/tex]
This means that the smallest value [tex]\( x \)[/tex] can take is 7. Any number greater than or equal to 7 will keep the expression inside the square root non-negative, making the square root defined.
Therefore, the domain of the function [tex]\( h(x) \)[/tex] is all [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
The correct answer is:
C. [tex]\( x \geq 7 \)[/tex]
The expression [tex]\( \sqrt{x - 7} \)[/tex] is only defined when the value inside the square root is non-negative. This means that:
[tex]\[ x - 7 \geq 0 \][/tex]
To solve this inequality for [tex]\( x \)[/tex], we add 7 to both sides:
[tex]\[ x \geq 7 \][/tex]
This means that the smallest value [tex]\( x \)[/tex] can take is 7. Any number greater than or equal to 7 will keep the expression inside the square root non-negative, making the square root defined.
Therefore, the domain of the function [tex]\( h(x) \)[/tex] is all [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
The correct answer is:
C. [tex]\( x \geq 7 \)[/tex]
