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

<math> f(g(x))</math>

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

<math>(f \circ g)(x) </math>

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)=f^r(x) can be derived from the rule for g given non-integer values of r. This is called fractional iteration[?].

See also:

• combinator
• lambda calculus