Is this map $\mathbb Q(x, y) \to \mathbb Q((t))$ well-defined?

Question

I am trying to find a map $\mathbb Q(x, y) \to \mathbb Q((t))$ and I have tried the map given by $x \mapsto \sum_{i > 0} t^i$ and $y \mapsto t^{-1}$. I know there is no ring map $\mathbb Q(x, y) \to \mathbb Q(t)$, so I need to use some infinite series somewhere in the definition, which lead me to this idea. Is this map well-defined?

Answer 1

Map $x \mapsto \displaystyle\sum_{i = 0}^{\infty} \frac{t^n}{n!}$, the Taylor series of $e^t$.