Let $f(x,y)=(\frac{1}{2} x^2 + x(y-1)^3, xy-x)$
(1) Find a formula for $f^{-1}$ in a small ball $B(b,r)$ where $b=(\frac{1}{2}, 0)$.
(2) Give an example of a radius $r>0$ for which the inverse function is well defined.
I showed that the inverse was well defined in some neighbourhood of b in a previous question using the Inverse Function Theorem.