funksion

Funksion is a term used in mathematics and computer science to describe a relation that assigns to every input element a single output element. Formally, a funksion f from a domain X to a codomain Y is denoted f: X -> Y, with f(x) belonging to Y for every x in X. The set X is called the domain of the funksion, and Y is the codomain. The actual outputs produced are called the range or image of the funksion.

A funksion is defined by its mapping rule, which must be well defined: each input in the domain is associated with exactly one output in the codomain. Common examples include f(x) = x^2 with domain R and codomain R, or the identity funksion id_X(x) = x on a set X. Functions can be classified by properties such as injectivity (distinct inputs map to distinct outputs), surjectivity (every element of the codomain is the image of some input), and bijectivity (both).

Operations on funksions include composition, where if f: X -> Y and g: Y -> Z, the composition g ∘ f: X -> Z assigns x to g(f(x)). A funksion is invertible if it is bijective, with an inverse funksion f^{-1}: Y -> X satisfying f^{-1}(f(x)) = x and f(f^{-1}(y)) = y. In calculus, functions are analyzed for continuity, differentiability, and limits. In programming, a funksion (function) is a block of code that takes inputs (parameters) and returns an output, and it can be pure (no side effects) or impure (may affect state).