Answer :
To determine the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], we need to find all the possible values of [tex]\( x \)[/tex] for which this function is defined.
The function involves a square root, and we know that you cannot take the square root of a negative number in the set of real numbers. Thus, the expression inside the square root, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero. This gives us the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
To solve this inequality, we add 7 to both sides:
[tex]\[ x \geq 7 \][/tex]
This means that the value of [tex]\( x \)[/tex] must be 7 or greater for the function to be defined. Thus, the domain of the function [tex]\( h(x) \)[/tex] is all real numbers [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
The correct choice from the given options is:
A. [tex]\( x \geq 7 \)[/tex]
The function involves a square root, and we know that you cannot take the square root of a negative number in the set of real numbers. Thus, the expression inside the square root, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero. This gives us the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
To solve this inequality, we add 7 to both sides:
[tex]\[ x \geq 7 \][/tex]
This means that the value of [tex]\( x \)[/tex] must be 7 or greater for the function to be defined. Thus, the domain of the function [tex]\( h(x) \)[/tex] is all real numbers [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
The correct choice from the given options is:
A. [tex]\( x \geq 7 \)[/tex]
