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Answer :
To determine the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], we need to ensure that the expression inside the square root is non-negative. This is because the square root function is only defined for non-negative numbers. Let's go through the steps:
1. Expression Inside the Square Root: The expression under the square root is [tex]\( x - 7 \)[/tex].
2. Set the Expression to be Non-negative: We need [tex]\( x - 7 \geq 0 \)[/tex].
3. Solve the Inequality: To find when [tex]\( x - 7 \geq 0 \)[/tex], solve the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
Add 7 to both sides to get:
[tex]\[
x \geq 7
\][/tex]
4. Conclusion: The domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex] is all values of [tex]\( x \)[/tex] for which [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is B. [tex]\( x \geq 7 \)[/tex].
1. Expression Inside the Square Root: The expression under the square root is [tex]\( x - 7 \)[/tex].
2. Set the Expression to be Non-negative: We need [tex]\( x - 7 \geq 0 \)[/tex].
3. Solve the Inequality: To find when [tex]\( x - 7 \geq 0 \)[/tex], solve the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
Add 7 to both sides to get:
[tex]\[
x \geq 7
\][/tex]
4. Conclusion: The domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex] is all values of [tex]\( x \)[/tex] for which [tex]\( x \geq 7 \)[/tex].
Therefore, the correct answer is B. [tex]\( x \geq 7 \)[/tex].
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