Answer :
To find the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex], we need to determine the values of [tex]\( x \)[/tex] for which the function is defined. The key thing to focus on is the square root part of the function, [tex]\(\sqrt{x-7}\)[/tex].
The expression inside the square root, [tex]\(x - 7\)[/tex], must be greater than or equal to zero because the square root of a negative number is not defined in the set of real numbers. Therefore, we set up the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
Now, let's solve this inequality for [tex]\( x \)[/tex]:
1. Add 7 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x \geq 7 \][/tex]
This tells us that the function is defined for all [tex]\( x \)[/tex] that are greater than or equal to 7. Therefore, the domain of the function [tex]\( h(x) \)[/tex] is all [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
In conclusion, the correct answer is:
B. [tex]\( x \geq 7 \)[/tex]
The expression inside the square root, [tex]\(x - 7\)[/tex], must be greater than or equal to zero because the square root of a negative number is not defined in the set of real numbers. Therefore, we set up the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
Now, let's solve this inequality for [tex]\( x \)[/tex]:
1. Add 7 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x \geq 7 \][/tex]
This tells us that the function is defined for all [tex]\( x \)[/tex] that are greater than or equal to 7. Therefore, the domain of the function [tex]\( h(x) \)[/tex] is all [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
In conclusion, the correct answer is:
B. [tex]\( x \geq 7 \)[/tex]
