Answer :
To determine the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex], we need to find all possible values of [tex]\( x \)[/tex] for which the function is defined.
1. Identify the Restriction:
- The square root function [tex]\(\sqrt{x-7}\)[/tex] is only defined for non-negative values. Therefore, the expression inside the square root, [tex]\(x - 7\)[/tex], must be greater than or equal to zero.
2. Set Up the Inequality:
- Write the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the Inequality:
- Add 7 to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x \geq 7
\][/tex]
4. Conclusion:
- The domain of the function [tex]\( h(x) \)[/tex] is all real numbers [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is B. [tex]\( x \geq 7 \)[/tex].
1. Identify the Restriction:
- The square root function [tex]\(\sqrt{x-7}\)[/tex] is only defined for non-negative values. Therefore, the expression inside the square root, [tex]\(x - 7\)[/tex], must be greater than or equal to zero.
2. Set Up the Inequality:
- Write the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the Inequality:
- Add 7 to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x \geq 7
\][/tex]
4. Conclusion:
- The domain of the function [tex]\( h(x) \)[/tex] is all real numbers [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is B. [tex]\( x \geq 7 \)[/tex].
