What is the inverse of the function $f: x \mapsto (x,x^{2}) : \mathbb{R} \to \mathbb{R}^{2}$?

Question

Let $f: x \mapsto (x,x^{2}) : \mathbb{R} \to \mathbb{R}^{2}$ and let $Y := f(\mathbb{R})$. Then $\mathbb{R}$ and $Y$ are in injection via $f$. Moreover, since $Y$ is the range of $f$, certainly $\mathbb{R}$ and $Y$ are in surjection via $f$. Therefore, the sets $\mathbb{R}$ and $Y$ are in bijection via $f$.

I am not sure how to write out the inverse of $f$ in the form $f^{-1}: (y_{1},y_{2}) \mapsto x: Y \to \mathbb{R}$.

Answer 1

What about $(y_1,y_2)\mapsto y_1$?