## Encyclopedia > Function composition

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# Function composition

In mathematics, a composite function, or composition of one function on another, represents the result (value) of one function used as the argument (i.e., the "input") to another.

In the expression

[itex] f(g(x))[/itex]

the value of g is the parameter of f, and the function f is composed on g. An equivalent representation is

[itex](f \circ g)(x) [/itex]

f.g is a function which is the composite function of f on g.

Derivatives of compositions involving differentiable functions can always be found using the chain rule.

The composition of a function on itself, such as f.f, is customarily written f2. (f.f)(x)=f(f(x))=f2(x). Likewise, (f.f.f)(x)=f(f(f(x)))=f3(x).

In some cases, an expression for f in g(x)=fr(x) can be derived from the rule for g given non-integer values of r. This is called fractional iteration[?].