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Functional Equations

I have been wondering how many functions satisfy these equations,

f (f (x))=f (x)

f (f (f (x))))=f (x) and so on.

Please help!!

Note by Abhi Kumbale
1 week, 5 days ago

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@Mr X
Can they be classified into certain classes? Abhi Kumbale · 1 week, 5 days ago

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f (x)=c where c is any real constant

and there's many other functions Mr X · 1 week, 5 days ago

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There are infinitely number of different functions. Mr X · 1 week, 5 days ago

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