noun For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ(B) = {x ∈ X : ƒ(x) ∈ B}.
The preimage of {4,9} under the function f:ℝ→ℝ:f(x)=x2 is the set {−3,−2,+2,+3}.