Which single sentence most precisely defines a one-to-one function (injective)?

A relation where every $x$ in the domain is matched with exactly one $y$ in the codomain and additionally every $y$ arises from exactly one $x$, so there are no repeated outputs and the mapping is reversible for all values in the range

A rule that produces an output for each input and may have outputs matched by multiple inputs as long as the domain is finite.

A function in which no two different inputs produce the same output

A mapping that pairs every element in the input set with at least one element in the output set, allowing duplicates in outputs but not in inputs