Question

Given f(x)=x^2-2 and g(x)= the square root of x-7, identify the composite function of g(f(x)) and it's correct domain

Answer 1

$g(f(x))=\sqrt{x^2-2-7}=\sqrt{x^2-9}\\\\ D:x^2-9\geq0\\ D:(x-3)(x+3)\geq0\\ D:x\in(-\infty,-3]\cup[3,\infty)$