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the following problem popped in a different thread but the original one went off-topic, and I thought this question deserved a thread itself:

Let's consider the entire set of the real functions [tex]f:\Re\rightarrow\Re[/tex]

A function [tex]f[/tex], with the property [tex]f=f^{-1}[/tex] is calledinvolution.

How many involutions is it possible to find in the set of real functions?

I know the following three forms: are there more?

[tex]f(x)=a-x[/tex]

[tex]f(x)=\frac{a}{x}[/tex]

[tex]f(x) = \frac{1}{x-a}+a[/tex]

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# Involutions (of real functions)

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