fonksiyon

In mathematics, a fonksiyon, or function, is a relation between two sets called the domain and the codomain that assigns to every element of the domain exactly one element of the codomain. It is usually written as f: X -> Y with the rule f(x) = y. The image of a value x is y, and the set of all such outputs is the range of f.

Functions can be classified by how they map inputs to outputs. An injective (one-to-one) function assigns distinct outputs to distinct inputs. A surjective (onto) function covers every element of the codomain. A bijective function is both injective and surjective and thus has an inverse function f^{-1}: Y -> X.

Composition of functions combines two functions f: X -> Y and g: Y -> Z into g ∘ f: X -> Z, where (g ∘ f)(x) = g(f(x)). The graph of a real-valued function is the set of points (x, f(x)) in the Cartesian plane.

Beyond pure mathematics, the notion of a function appears in computer science as a block of code that maps inputs to outputs. In programming, functions may be pure (no side effects) or impure, and they can be defined by rules, algorithms, or data structures.

Key concepts include domain, codomain, image, range, and inverse, as well as limits, continuity, and differentiability when the codomain is the real numbers. Functions can be total (defined for all domain elements) or partial (defined only for a subset of the domain). In Turkish, fonksiyon means function.