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In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function. For instance, the functions and can be ''composed'' to yield a function which maps in to in . Intuitively, if is a function of , and is a function of , then is a function of . The resulting ''composite'' function is denoted , defined by for all in .〔Some authors use , defined by instead.〕 The notation is read as " circle ", or " round ", or " composed with ", " after ", " following ", or " of ", or " on ". Intuitively, composing two functions is a chaining process in which the output of the first function becomes the input of the second function. The composition of functions is a special case of the composition of relations, so all properties of the latter are true of composition of functions. The composition of function has some additional properties. ==Examples== * Composition of functions on a finite set: If , and , then . * Composition of functions on an infinite set: If (where is the set of all real numbers) is given by and is given by , then: :, and :. * If an airplane's elevation at time is given by the function , and the oxygen concentration at elevation is given by the function , then describes the oxygen concentration around the plane at time . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Function composition」の詳細全文を読む スポンサード リンク
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