Where is the mapping invertible in region?

Question

Consider $G(x, y) = ((x-1)^2, y^4)$, for which point(s) $\overrightarrow{b} \in \mathbb{R}^2$ is $G$ invertible in the neighbourhood of $b$?

I dont see a trick as to how we can find the point. Can someone provide a hint?

Answer 1

Find the Jacobian matrix. Find its determinant $D(x,y)$. Then $G$ is locally invertible at all $b$ such that $D(b) \neq 0$ (by inverse function theorem)