Answer :
To determine the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex], we need to focus on the square root part [tex]\(\sqrt{x-7}\)[/tex].
1. Identify domain restrictions: The expression inside the square root needs to be non-negative, meaning it cannot be less than zero. So, we set up the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve the inequality: To find [tex]\( x \)[/tex], add 7 to both sides:
[tex]\[
x \geq 7
\][/tex]
3. Conclusion: The domain of the function [tex]\( h(x) \)[/tex] is all [tex]\( x \)[/tex] values that satisfy [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is option D: [tex]\( x \geq 7 \)[/tex].
1. Identify domain restrictions: The expression inside the square root needs to be non-negative, meaning it cannot be less than zero. So, we set up the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve the inequality: To find [tex]\( x \)[/tex], add 7 to both sides:
[tex]\[
x \geq 7
\][/tex]
3. Conclusion: The domain of the function [tex]\( h(x) \)[/tex] is all [tex]\( x \)[/tex] values that satisfy [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is option D: [tex]\( x \geq 7 \)[/tex].
