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.
1. Focus on the square root part: 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.
2. Set up the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the inequality for [tex]\( x \)[/tex]:
[tex]\[
x \geq 7
\][/tex]
4. Conclusion: The domain of the function [tex]\( h(x) \)[/tex] is the set of all [tex]\( x \)[/tex] values that satisfy the inequality [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( x \geq 7 \)[/tex]
1. Focus on the square root part: 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.
2. Set up the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the inequality for [tex]\( x \)[/tex]:
[tex]\[
x \geq 7
\][/tex]
4. Conclusion: The domain of the function [tex]\( h(x) \)[/tex] is the set of all [tex]\( x \)[/tex] values that satisfy the inequality [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( x \geq 7 \)[/tex]
