Definition:Inverse Mapping/Also defined as

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

Then its inverse mapping is the mapping $g$ such that:
 * $(1): \quad$ its domain $\Dom g$ equals the image $\Img f$ of $f$
 * $(2): \quad \forall y \in \Img f: \map f {\map g y} = y$

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.