The inverse of function:

Concept: For a bijective function f : A → B (one-to-one and onto), the inverse f-1 : B → A is defined by assigning to every element b of the codomain B the unique element a of the domain A such that f(a) = b. Injectivity of f guarantees at most one such a; surjectivity guarantees at least one; together they guarantee exactly one — so f-1(b) is always a single, well-defined element of A.

Application: The stem asks what the inverse of a function does. Matching the definition above, the inverse takes an input from the codomain and produces a single, uniquely-determined output in the domain — that is, it maps each element of the codomain to a unique element of the domain.

Cross-check: Take a concrete bijection f : ℝ → ℝ, f(x) = 2x + 3. For any codomain value y, solving y = 2x + 3 gives x = (y − 3) / 2 — exactly one x for every y. This confirms the inverse runs from the codomain to the domain and lands on a single, unique domain element each time, matching the definition.

Contrasting the other statements:

• Both “Reverses the mapping, producing a new mapping from the domain to the codomain” and “Maps each element of the domain to a unique element of the codomain” describe a resulting correspondence running in the domain-to-codomain direction — the same direction as the original function f — so neither describes a reversal of f's direction.

• “Reverses the mapping, producing a new mapping from the codomain to the domain” does state the correct direction (codomain to domain), but only as a general description of that direction. It does not specify the precise rule — landing on one particular domain element for every codomain element — that the standard definition of the inverse of a function requires.

Hence: the inverse of a function maps each element of the codomain to a unique element of the domain.