The function [tex]f(x)=x^2-2[/tex] is defined for every real number (It is a polynomial function).
But we have :
[tex]\forall x\in\mathbb R,\quad x^2\ge0[/tex]
so :
[tex]\forall x\in\mathbb R,\quad x^2-2\ge-2[/tex]
Therefore ;
domain of f is all real number , range of is y≥-2
domain of f^-1 is x≥-2 , range of f^-1 is all real number
