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In [[mathematics]], if a [[Function (mathematics)|function]] <code>f(x)=y</code> is [[Injective function|injective]], exactly one function <code>g(y)</code> will exist such that <code>g(y)=x</code>, otherwise no such function will exist.

The function <code>g(y)</code> is called the inverse function of <code>f(x)</code> because it "reverses" <code>f(x)</code>; that is to say <code>g(f(x))=x</code>.

== See also ==

* [[Function (mathematics)]]
* [[Injective function]]
* [[Inverse function theorem]], gives sufficient conditions for a function to be invertible in a neighborhood of a point in its domain and gives a formula for the derivative of the inverse function
* [[Inverse functions and differentiation]]
* [[Inverse relation]]
* [[Lagrange inversion theorem]], gives the Taylor series expansion of the inverse function of an analytic function

== External links ==

* [https://en.wikipedia.org/wiki/Inverse_function Inverse function] @ Wikipedia


[[Category:Mathematics]]