Given function [tex]f(x)=x^2-4[/tex] find its inverse by substituting x for f(x) and then solving for f(x).
[tex]x=f(x)^2-4\implies f(x)^{-1}=\sqrt{x+4}[/tex]
Where [tex]x+4>=0[/tex] for x to be real.
So solve the inequality and you will obtain the domain:
[tex]x+4>=0\implies x>=-4\implies x\in[-4,+\infty)[/tex].
Range is equal to the range of square root function,
[tex]y\in[0, +\infty)[/tex].
Hope this helps.
