Question

Find the domain of the function using interval notation. "TexFormula1" title="f(x)=8\sqrt{x-9}" alt="f(x)=8\sqrt{x-9}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

D_{f(x)} = [9, \infty)

Step-by-step explanation:

Here we have the square root of a function, in the following format:

$f(x) = \sqrt{g(x)}$

For the square root, and roots of even numbers(root of 4, 6, ...), we have the following condition in the domain

$g(x) \geq 0$

In this problem, we have that:

$f(x) = 8\sqrt{x-9}$

So

$x - 9 \geq 0$

$x \geq 9$

So the domain is

$D_{f(x)} = [9, \infty)$