Encyclopedia > Function composition

  Article Content

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

See also:



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
581

... 530s 540s 550s 560s 570s - 580s - 590s 600s 610s 620s 630s Years: 576 577 578 579 580 581 582 583 584 585 586 Events The Sui Dynasty replaces the Northern ...