Answer:
All real numbers [tex]\left|x\right|\ge2[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x^{2}[/tex]
[tex]g(x)=\sqrt{x-4}[/tex]
we know that
To obtain g(f(x)), substitute the variable x in the function g(x) by the function f(x)
so
[tex]g(f(x))=\sqrt{x^{2}-4}[/tex]
To determine the domain, remember that the radicand must be greater than or equal to zero
[tex]x^{2}-4\geq 0[/tex]
Adds 4 both sides
[tex]x^{2}\geq 4[/tex]
square root both sides
The solutions are
[tex]x\geq 2[/tex]
[tex]x\leq -2[/tex]
The domain is
(-∞,-2] ∪ [2,∞)
This expression is equivalent to say
All real numbers [tex]\left|x\right|\ge2[/tex]
