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. This is because the square root function is defined only for non-negative numbers.
1. Set up the inequality for the radicand (the expression inside the square root):
[tex]$$
x - 7 \geq 0.
$$[/tex]
2. Solve the inequality:
[tex]$$
x \geq 7.
$$[/tex]
This means that [tex]$x$[/tex] can be any real number greater than or equal to 7. Thus, the domain of the function is all real numbers [tex]$x$[/tex] such that [tex]$x \geq 7$[/tex].
The correct answer is:
[tex]$$
\boxed{x \geq 7.}
$$[/tex]
[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 defined only for non-negative numbers.
1. Set up the inequality for the radicand (the expression inside the square root):
[tex]$$
x - 7 \geq 0.
$$[/tex]
2. Solve the inequality:
[tex]$$
x \geq 7.
$$[/tex]
This means that [tex]$x$[/tex] can be any real number greater than or equal to 7. Thus, the domain of the function is all real numbers [tex]$x$[/tex] such that [tex]$x \geq 7$[/tex].
The correct answer is:
[tex]$$
\boxed{x \geq 7.}
$$[/tex]
