Answer :
To find the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex], we need to focus on the square root part of the function, [tex]\(\sqrt{x-7}\)[/tex].
Here's a step-by-step solution:
1. Identify the condition for the square root:
The expression inside the square root, [tex]\( x - 7 \)[/tex], must be non-negative because the square root of a negative number is not defined in the set of real numbers. This gives us the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve the inequality:
Add 7 to both sides of the inequality to solve for [tex]\( x \)[/tex]:
[tex]\[
x \geq 7
\][/tex]
3. Determine the domain:
Based on the inequality [tex]\( x \geq 7 \)[/tex], the function is defined for all real numbers [tex]\( x \)[/tex] that are greater than or equal to 7.
Thus, the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex] is [tex]\( x \geq 7 \)[/tex], corresponding to option B.
Here's a step-by-step solution:
1. Identify the condition for the square root:
The expression inside the square root, [tex]\( x - 7 \)[/tex], must be non-negative because the square root of a negative number is not defined in the set of real numbers. This gives us the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve the inequality:
Add 7 to both sides of the inequality to solve for [tex]\( x \)[/tex]:
[tex]\[
x \geq 7
\][/tex]
3. Determine the domain:
Based on the inequality [tex]\( x \geq 7 \)[/tex], the function is defined for all real numbers [tex]\( x \)[/tex] that are greater than or equal to 7.
Thus, the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex] is [tex]\( x \geq 7 \)[/tex], corresponding to option B.
