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Answer :
To find the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], we need to consider the part of the function inside the square root, because a square root is only defined for non-negative numbers.
Here's how to determine the domain:
1. Identify the expression inside the square root: In the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], the expression inside the square root is [tex]\( x - 7 \)[/tex].
2. Set up an inequality for the expression inside the square root: Since square roots are only defined for non-negative values, we need:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the inequality: To find the values of [tex]\( x \)[/tex] that satisfy this inequality, solve for [tex]\( x \)[/tex]:
[tex]\[
x \geq 7
\][/tex]
4. Conclude the domain: The solution to the inequality tells us that [tex]\( x \)[/tex] can be any real number greater than or equal to 7. Therefore, the domain of the function [tex]\( h(x) \)[/tex] is:
[tex]\[
x \geq 7
\][/tex]
This means the correct answer is:
B. [tex]\( x \geq 7 \)[/tex]
Here's how to determine the domain:
1. Identify the expression inside the square root: In the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], the expression inside the square root is [tex]\( x - 7 \)[/tex].
2. Set up an inequality for the expression inside the square root: Since square roots are only defined for non-negative values, we need:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the inequality: To find the values of [tex]\( x \)[/tex] that satisfy this inequality, solve for [tex]\( x \)[/tex]:
[tex]\[
x \geq 7
\][/tex]
4. Conclude the domain: The solution to the inequality tells us that [tex]\( x \)[/tex] can be any real number greater than or equal to 7. Therefore, the domain of the function [tex]\( h(x) \)[/tex] is:
[tex]\[
x \geq 7
\][/tex]
This means the correct answer is:
B. [tex]\( x \geq 7 \)[/tex]
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