Inverse function: Difference between revisions

Revision as of 19:21, 3 July 2024

Revision as of 08:25, 4 July 2024

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[[Image:Inverse Function.png|thumb|right|A function {{mvar|f}} and its inverse {{math|''f''⁻¹}}. Because {{mvar|f}} maps {{mvar|a}} to 3, the inverse {{math|''f''⁻¹}} maps 3 back to {{mvar|a}}.]]

{{Functions}}

In [[mathematics]], the '''inverse function''' of a [[Function (mathematics)|function]] {{Mvar|f}} (also called the '''inverse''' of {{Mvar|f}}) is a [[function (mathematics)|function]] that undoes the operation of {{Mvar|f}}. The inverse of {{Mvar|f}} exists [[if and only if]] {{Mvar|f}} is [[Bijection|bijective]] (no output is produced by two inputs), and if it exists, is denoted by <math>f^{-1} .</math>

For a function <math>f\colon X\to Y</math>, its inverse <math>f^{-1}\colon Y\to X</math> admits an explicit description: it sends each element <math>y\in Y</math> to the unique element <math>x\in X</math> such that {{Math|1=''f''(''x'') = ''y''}}.