Does injective imply each $x$ matches to a unique $y$?

Question

Injective means one-to-one matching, as in each $y$ is matched by only one $x$. However, does this mean that each $x$ matches only to one $y$?

Answer 1

In any function $x$ matches to only one $y$. That's literally the definition of a function

Answer 2

This property of each x mapping to only one y is officially called "well-definedness", and every function (even linear maps defined by matrices) ought to satisfy it before any math can be done with the function. Every injective function is (implicitly) already well-defined.