Function composition is an operation that takes two functions, f and g, and produces a new function f-of-g, so that evaluating the composite function at an input x gives f applied to g applied to x, meaning g is applied first and f is applied to the result. The composition of functions is a special case of the more general composition of relations, and as a result every property of the composition of relations, including associativity, also holds for the composition of functions.
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Source Function Composition (Wikipedia)
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1. Wolfram MathWorld: Function Composition -- from Wolfram MathWorld
Wolfram MathWorldSubject classificationsQuote, Subject classifications
Algebra Algebraic Operations General Algebraic Operations
Function Composition (Wikipedia)
Wikimedia FoundationLead section
As a result, all properties of composition of relations are true of composition of functions, such as associativity.
Associated With: Functions, Lead section, first sentence
the composition operator ∘ takes two functions, f and g, and returns a new function f∘g
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