Prove that, given an algebraic plane curve $X$, the map $f: \mathbb{A}^1 \to X$ defined as $f(t) = (t^2, t^3)$ and the map $f: \mathbb{A}^1 \to X$ defined as $g(t) = (t^2 - 1, t(t^2 -1))$ are birational.
My attempt For the first one I wrote $x= t^2$ and $y=t^3$ and then $\frac{y}{x}= t$. I think I can’t go on from here, I don’t even know if expressing $t$ in terms of only $x$ and $y$ is helpful.