Definition

Composite Function

A composite function is created when one function is applied to the result of another function. For two functions ff and gg, the composite function fgf \circ g is defined by (fg)(x)=f(g(x))(f \circ g)(x) = f(g(x)), which means the output of gg is used as the input of ff. The notation fgf \circ g is read as 'ff composed with gg' or 'ff of gg.' It is important to note that (fg)(x)(f \circ g)(x) is different from the product of two functions (fg)(x)(f \cdot g)(x): composition means substituting one function into the other, whereas multiplication means multiplying the output values of the two functions together. Additionally, function composition is generally not commutative — the order in which functions are composed matters, so (fg)(x)(f \circ g)(x) does not necessarily equal (gf)(x)(g \circ f)(x).

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Updated 2026-05-26

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