Inverse of function $f: \mathbb{R}^3 \rightarrow \mathbb{R}$.

Question

I'm really confused right now, does there exist an inverse $f^{-1}$ to the function $f(x,y,z) = x^2+y^2-1$. Thanks for clearing it up.

Answer 1

Notice that $f(1,-1,0)=f(-1,1,0)$. So, $f$ is not one-to-one and hence cannot be invertible.