Answer :
Sure! Let's determine the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex].
1. Understand the function type: The function involves a square root, [tex]\(\sqrt{}\)[/tex], which is defined only for non-negative numbers. This means the expression inside the square root must be greater than or equal to zero.
2. Set up the inequality:
- We have the expression [tex]\( x - 7 \)[/tex] inside the square root.
- We need to solve [tex]\( x - 7 \geq 0 \)[/tex].
3. Solve the inequality:
- Add 7 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x - 7 + 7 \geq 0 + 7
\][/tex]
[tex]\[
x \geq 7
\][/tex]
4. Conclusion:
- The domain of the function [tex]\( h(x) \)[/tex] is all [tex]\( x \)[/tex] values such that [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is C. [tex]\( x \geq 7 \)[/tex].
1. Understand the function type: The function involves a square root, [tex]\(\sqrt{}\)[/tex], which is defined only for non-negative numbers. This means the expression inside the square root must be greater than or equal to zero.
2. Set up the inequality:
- We have the expression [tex]\( x - 7 \)[/tex] inside the square root.
- We need to solve [tex]\( x - 7 \geq 0 \)[/tex].
3. Solve the inequality:
- Add 7 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x - 7 + 7 \geq 0 + 7
\][/tex]
[tex]\[
x \geq 7
\][/tex]
4. Conclusion:
- The domain of the function [tex]\( h(x) \)[/tex] is all [tex]\( x \)[/tex] values such that [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is C. [tex]\( x \geq 7 \)[/tex].
