# Inverse

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The **inverse** of a function is a function that undoes its effect, computing an argument that corresponds to the given result for that function. In APL it's usually written with the Power operator as `(f⍣¯1) x`

. While some functions such as Reverse have an obvious exact inverse, others might have no valid inverse or many possible choices for a given result. Treatment of these cases varies among dialects, but a common rule is that the inverse should satisfy `x ≡ f (f⍣¯1) x`

, making it a right inverse in mathematical terminology. A stand-alone inverse operator is defined in Kap (`˝`

), BQN ("Undo", `⁼`

), and Uiua ("Un", `°`

).

As with Power in general, the dyadic inverse `⍺(f⍣¯1)⍵`

is defined to be the inverse of `⍺∘f`

, that is, `(⍺∘f⍣¯1)⍵`

.

## External links

### Lessons

- APL Cultivation 34