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Answer :
To determine the domain of the function [tex]\( n'(x) = \sqrt{x - 7} + 5 \)[/tex], we need to ensure that all parts of the function are defined for the values of [tex]\( x \)[/tex] we consider.
1. Identify the parts of the function: The function involves a square root, [tex]\(\sqrt{x - 7}\)[/tex].
2. Determine the requirement for the square root: For the square root to be defined, the expression inside it must be non-negative. This means:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
Adding 7 to both sides gives:
[tex]\[
x \geq 7
\][/tex]
4. Conclusion about the domain: The function [tex]\( n'(x) = \sqrt{x - 7} + 5 \)[/tex] is defined for all values of [tex]\( x \)[/tex] where [tex]\( x \geq 7 \)[/tex].
Therefore, the domain of the function is [tex]\( x \geq 7 \)[/tex], which corresponds to option A.
1. Identify the parts of the function: The function involves a square root, [tex]\(\sqrt{x - 7}\)[/tex].
2. Determine the requirement for the square root: For the square root to be defined, the expression inside it must be non-negative. This means:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the inequality:
[tex]\[
x - 7 \geq 0
\][/tex]
Adding 7 to both sides gives:
[tex]\[
x \geq 7
\][/tex]
4. Conclusion about the domain: The function [tex]\( n'(x) = \sqrt{x - 7} + 5 \)[/tex] is defined for all values of [tex]\( x \)[/tex] where [tex]\( x \geq 7 \)[/tex].
Therefore, the domain of the function is [tex]\( x \geq 7 \)[/tex], which corresponds to option A.
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