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There are terms for various kinds of functions (or operators) such as...

associative - (a # b) # c  =  a # (b # c)
commutative - a # b  =  b # a
idempotent  - f (f (x)) = f (x)

Is there a similar name for functions that are their own inverse?

f (f (x)) = x
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marked as duplicate by Najib Idrissi, Arctic Char, Clayton, Joel Reyes Noche, George Simpson Aug 31 '15 at 13:05

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

up vote 14 down vote accepted

It is called as an involution.

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Thanks - have to wait a few minutes before I can accept, but this is the answer. – Steve314 Sep 27 '13 at 17:05
1  
Some examples of involutions are shown here – Mufasa Sep 27 '13 at 17:08
    
The most trivial involution is f(x) = x. – Tortoise Sep 27 '13 at 23:00

Such a function is called an involution.

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