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

$g(f(x))=\sqrt{x^2-2-7}=\sqrt{x^2-9}\\ D_f:x^2-9\geq0\\ D_f:x^2\geq9\\ D_f:x\geq 3 \vee x\leq-3\\ D_f:x\in(\infty,-3]\cup[3,\infty)$