Inverse function theorem and finding the open set that allows $f$ to have a local inverse

Question

The inverse function theorem says that there exists an open set $U$ such that there is a local inverse of $f$ around a point $a$.
However, how would we actually find an open set containing this point $a$?
In particular, the function
$$f(x,y) = \begin{pmatrix} x^2 y + 2y - x \\ 3xy + 4x \end{pmatrix}$$ with the point $(0,0)$.