Answer :
To find 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, because you cannot take the square root of a negative number in the set of real numbers.
1. Start with the expression inside the square root:
[tex]\[
x - 7
\][/tex]
2. Set up the inequality to ensure the expression is non-negative:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the inequality for [tex]\( x \)[/tex]:
- Add 7 to both sides:
[tex]\[
x \geq 7
\][/tex]
The inequality [tex]\( x \geq 7 \)[/tex] indicates that the domain of the function [tex]\( h(x) \)[/tex] is all real numbers greater than or equal to 7.
Therefore, the domain of the function is:
D. [tex]\( x \geq 7 \)[/tex]
This means the function is defined for any value of [tex]\( x \)[/tex] that is greater than or equal to 7.
1. Start with the expression inside the square root:
[tex]\[
x - 7
\][/tex]
2. Set up the inequality to ensure the expression is non-negative:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the inequality for [tex]\( x \)[/tex]:
- Add 7 to both sides:
[tex]\[
x \geq 7
\][/tex]
The inequality [tex]\( x \geq 7 \)[/tex] indicates that the domain of the function [tex]\( h(x) \)[/tex] is all real numbers greater than or equal to 7.
Therefore, the domain of the function is:
D. [tex]\( x \geq 7 \)[/tex]
This means the function is defined for any value of [tex]\( x \)[/tex] that is greater than or equal to 7.
