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Answer :
To find the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex], we need to consider the expression inside the square root: [tex]\( x - 7 \)[/tex].
The square root function is only defined for non-negative numbers. This means the expression inside the square root, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero for the function to be defined.
Let's set up the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
Now, solve for [tex]\( x \)[/tex]:
1. Add 7 to both sides of the inequality:
[tex]\[ x \geq 7 \][/tex]
This tells us that [tex]\( x \)[/tex] must be greater than or equal to 7 for the function [tex]\( h(x) \)[/tex] to have real values.
So, the domain of the function [tex]\( h(x) \)[/tex] is all values of [tex]\( x \)[/tex] that are greater than or equal to 7. In set notation, this is written as [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( x \geq 7 \)[/tex]
The square root function is only defined for non-negative numbers. This means the expression inside the square root, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero for the function to be defined.
Let's set up the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
Now, solve for [tex]\( x \)[/tex]:
1. Add 7 to both sides of the inequality:
[tex]\[ x \geq 7 \][/tex]
This tells us that [tex]\( x \)[/tex] must be greater than or equal to 7 for the function [tex]\( h(x) \)[/tex] to have real values.
So, the domain of the function [tex]\( h(x) \)[/tex] is all values of [tex]\( x \)[/tex] that are greater than or equal to 7. In set notation, this is written as [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( x \geq 7 \)[/tex]
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