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Function composition. In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function. For instance, the functions f : X â Y and g : Y â Z can be composed to yield a function which maps x in X to g(f(x)) in Z.
Considering a function as a special case of a binary relation (namely functional relations), function composition satisfies the definition for relation composition. The composition is defined in the same way for partial functions and Cayley's theorem has its analogue called Wagner-Preston theorem.