Answer:
D_{f(x)} = [9, \infty)
Step-by-step explanation:
Here we have the square root of a function, in the following format:
[tex]f(x) = \sqrt{g(x)}[/tex]
For the square root, and roots of even numbers(root of 4, 6, ...), we have the following condition in the domain
[tex]g(x) \geq 0[/tex]
In this problem, we have that:
[tex]f(x) = 8\sqrt{x-9}[/tex]
So
[tex]x - 9 \geq 0[/tex]
[tex]x \geq 9[/tex]
So the domain is
[tex]D_{f(x)} = [9, \infty)[/tex]
