Answer :
To find the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], we need to look at the part under the square root, which is [tex]\( x - 7 \)[/tex].
For the square root to be defined and produce real numbers, the expression inside the square root must be non-negative (i.e., greater than or equal to zero). So, we set up the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
Next, solve this inequality for [tex]\( x \)[/tex]:
1. Add 7 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x \geq 7 \][/tex]
This inequality means that [tex]\( x \)[/tex] must be greater than or equal to 7 for the function [tex]\( h(x) \)[/tex] to be defined.
Therefore, the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex] is all real numbers [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
The correct answer is:
A. [tex]\( x \geq 7 \)[/tex]
For the square root to be defined and produce real numbers, the expression inside the square root must be non-negative (i.e., greater than or equal to zero). So, we set up the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
Next, solve this inequality for [tex]\( x \)[/tex]:
1. Add 7 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x \geq 7 \][/tex]
This inequality means that [tex]\( x \)[/tex] must be greater than or equal to 7 for the function [tex]\( h(x) \)[/tex] to be defined.
Therefore, the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex] is all real numbers [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
The correct answer is:
A. [tex]\( x \geq 7 \)[/tex]
