Definition:Inverse Mapping/Also defined as

Definition
Let $S$ and $T$ be sets.

Let $f: S \to T$ be an injection.

Then its inverse mapping is the mapping $g$ such that:
 * its domain $\operatorname{Dom} \left({g}\right)$ equals the image $\operatorname{Im} \left({f}\right)$ of $f$
 * $\forall y \in \operatorname{Im} \left({f}\right): f \left({g \left({y}\right)}\right) = y$

Thus $f$ is seen to be a surjection by tacit use of Restriction of Mapping to Image is Surjection.

does not endorse this approach, and considers that its use can cause important insight to be missed.