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preimage
This term is used exclusively within the technical register of mathematics, specifically in set theory and function analysis. It describes the inverse mapping process, identifying all inputs that produce a particular output. While "inverse image" is a common synonym, "preimage" is often preferred for its conciseness in formal proofs and textbooks.
Because it refers to a set of elements, the term remains conceptually linked to the domain of a function. Even if the preimage contains only a single element, it is formally treated as a set, which is a critical distinction when performing operations in higher-level algebra or topology.