Question

I need help ASAP!!!!!Will mark answer with the best explanation as Brainliest!!!!!!

Answer 1

Answer:

All real numbers $\left|x\right|\ge2$

Step-by-step explanation:

we have

$f(x)=x^{2}$

$g(x)=\sqrt{x-4}$

we know that

To obtain g(f(x)), substitute the variable x in the function g(x) by the function f(x)

so

$g(f(x))=\sqrt{x^{2}-4}$

To determine the domain, remember that the radicand must be greater than or equal to zero

$x^{2}-4\geq 0$

Adds 4 both sides

$x^{2}\geq 4$

square root both sides

The solutions are

$x\geq 2$

$x\leq -2$

The domain is

(-∞,-2] ∪ [2,∞)

This expression is equivalent to say

All real numbers $\left|x\right|\ge2$