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Invertible function : ウィキペディア英語版
Inverse function

In mathematics, an inverse function is a function that "reverses" another function. That is, if is a function mapping to , then the inverse function of maps back to .
==Definitions==

Let be a function whose domain is the set , and whose image (range) is the set . Then is ''invertible'' if there exists a function with domain and image , with the property:
:f(x) = y\,\,\Leftrightarrow\,\,g(y) = x.
If is invertible, the function is unique, which means that there is exactly one function satisfying this property (no more, no less). That function is then called ''the'' inverse of , and is usually denoted as .
Stated otherwise, a function is invertible if and only if its inverse relation is a function on the range , in which case the inverse relation is the inverse function.
Not all functions have an inverse. For this rule to be applicable, each element must correspond to no more than one ; a function with this property is called one-to-one or an injection. If and are functions on and respectively, then both are bijections. The inverse of an injection that is not a bijection is a partial function, that means for some it is undefined.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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