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In [[mathematics]], if ƒ is a [[function]] from a set A to a set B, then an '''inverse''' [[function]] for ƒ is a function from B  to A, with the property that a round trip (a [[composition]]) from A to B to A (or from B to A to B) returns each element of the initial set to itself. Thus, if an input x into the [[function]] ƒ produces an output y, then inputting y into the inverse function produces the output x, and vice versa.

In [[mathematics]], if ƒ is a [[function]] from a set A to a set B, then an '''inverse''' [[function]] for ƒ is a function from B  to A, with the property that a round trip (a [[composition]]) from A to B to A (or from B to A to B) returns each element of the initial set to itself. Thus, if an input x into the [[function]] ƒ produces an output y, then inputting y into the inverse function produces the output x, and vice versa.

A [[function]] ƒ that has an inverse is called invertible; the inverse function is then [[uniquely]] determined by ƒ and is denoted by ƒ−1 (read f inverse, not to be confused with [http://en.wikipedia.org/wiki/Exponentiation exponentiation]).

A [[function]] ƒ that has an inverse is called invertible; the inverse function is then [[uniquely]] determined by ƒ and is denoted by ƒ−1 (read f inverse, not to be confused with [https://en.wikipedia.org/wiki/Exponentiation exponentiation]).

*Definition

*Definition

Let ƒ be a [[function]] whose [[domain]] is the set X, and whose [http://en.wikipedia.org/wiki/Codomain codomain] is the set Y. Then, if it exists, the inverse of ƒ is the function ƒ−1 with domain Y and codomain X, with the property:

Let ƒ be a [[function]] whose [[domain]] is the set X, and whose [https://en.wikipedia.org/wiki/Codomain codomain] is the set Y. Then, if it exists, the inverse of ƒ is the function ƒ−1 with domain Y and codomain X, with the property:

[[File:Inverse.jpg]]

[[File:Inverse.jpg]]

Stated otherwise, a [[function]] is invertible if and only if its inverse [[relation]] is a [[function]], in which case the inverse relation is the inverse function.[http://en.wikipedia.org/wiki/Inverse_function]

Stated otherwise, a [[function]] is invertible if and only if its inverse [[relation]] is a [[function]], in which case the inverse relation is the inverse function.[https://en.wikipedia.org/wiki/Inverse_function]

[[Category: Mathematics]]

[[Category: Mathematics]]