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 f( f(x) ) = x bo198214 Administrator Posts: 1,395 Threads: 91 Joined: Aug 2007 04/17/2009, 09:59 AM (This post was last modified: 04/17/2009, 10:00 AM by bo198214.) tommy1729 Wrote:f(x) =/= x f(f(x)) = x exp(f(x)) = f(exp(x)) give examples of Coo f(x) satisfying all the above 3 equations at once. It may be interesting for you that there is no continuous solution of $f(f(f(x)))=x$. And that each solution of $f(f(x))=x$ is strictly decreasing with a fixed point. You can read further on this subject (keyword Babbage equation, involution) in Kuczma, Iterative functional equations. « Next Oldest | Next Newest »

 Messages In This Thread f( f(x) ) = x - by tommy1729 - 04/15/2009, 04:37 PM RE: f( f(x) ) = x - by andydude - 04/17/2009, 03:36 AM RE: f( f(x) ) = x - by bo198214 - 04/17/2009, 09:59 AM

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