Funksie

Funksie, in mathematical and computing contexts generally written as function in English, is a relation that assigns to each element of a set of inputs a single element of a set of outputs. A function f from a domain X to a codomain Y is often written as f: X → Y, with f(x) ∈ Y for every x ∈ X. The domain is the set of allowable inputs, the codomain is the set of possible outputs, and the actual outputs f(X) form the range.

A function is well-defined when every input has exactly one output. Functions can be total, defined for all elements of the domain, or partial, defined only on a subset. Important classifications include injective (one-to-one, no two inputs map to the same output), surjective (onto, every element of the codomain is hit by some input), and bijective (both injective and surjective, with a true inverse).

Examples illustrate these ideas: f(x) = x^2 with domain R to R is not injective, since f(1) = f(-1). The function g(x) = x + 1 is bijective from R to R, with inverse g^-1(y) = y - 1. Function composition, (f ∘ g)(x) = f(g(x)), combines mappings, and inverse functions exist only for bijections.

In computer science, a function (or method) maps inputs to outputs and may have side effects or be a pure function without them. Functions are fundamental in algorithms, data transformation, and modeling relationships in science and engineering. The Afrikaans term for function is funksie. See also: function (mathematics), mapping, inverse function.