Meaning of preimage | Babel Free

Definitions

For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ⁻¹(B) = {x ∈ X : ƒ(x) ∈ B}.

Equivalents

Examples

“The preimage of #92;#123;4,9#92;#125; under the function f#58;#92;R#92;rightarrow#92;R#58;f(x)#61;x² is the set #92;#123;-3,-2,#43;2,#43;3#92;#125;.”

“1967 [Academic Press], Francois Treves, Topological Vector Spaces, Distributions and Kernels, 2006, Dover, page 22, The preimage of a neighborhood U of 0 in E must be a neighborhood of (0,x), since (0,x) is mapped into 0.”

“Previously, maps and hypermaps were constructed as the preimages of a segment joining two of the three critical values.”

“Loosely speaking, saying that a function f is one-way implies that given y (in the range of f) it is infeasible to find a preimage of y under f.”

CEFR level