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What is the name of the property of a function that yields the original result when done twice in a row:

$$f(f(x)) = x?$$

I'm pretty sure there is a word for these functions, but I haven't been able to find it.

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    $\begingroup$ The are often called involutions (which generally means something that squares to the identity). $\endgroup$ – Tobias Kildetoft May 9 '16 at 8:01
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A function that has this property is known as an involution.

Such functions are interesting to study, as they are their own inverse $$f^{-1}(x) = f(x)$$

Some examples:$$f(x) = x\\f(x) = \frac{a}{x}\\f(x) = a - x\\f(x) = a + \frac{b}{x-a}$$

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    $\begingroup$ Further examples in $\Bbb R^n$ can be found here $\endgroup$ – Surb May 9 '16 at 8:12
  • $\begingroup$ Exactly what I was looking for, thanks. $\endgroup$ – Baptiste Wicht May 9 '16 at 8:24

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