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 Function(Function()) Finding (Posted on 2005-02-02)
If f(x)=1-x, f(f(x))=x. Can you provide another such f(x), other than the obvious f(x)=x or f(x)=-x?

Can you find a real function g(x) such that g(g(x))=-x? Note that if we allowed complex numbers, g(x)=ix would do the job.

Can you find another real function h(x) so for x≠0, h(h(x))=1/x?

In all cases, if you cannot find a solution that works for all x, a function valid for some ranges is better than nothing!

 See The Solution Submitted by Old Original Oskar! Rating: 3.1667 (6 votes)

 Subject Author Date f(x) Math Man 2013-05-14 12:22:27 re: a working function fore f(x) Dimmeh 2005-08-22 10:35:48 Here's an infinte number of f(x) that all work!!! Dimmeh 2005-08-22 10:35:09 a working function fore f(x) mates catalin 2005-02-26 12:06:18 re: a function for F(x), for G(x) Federico Kereki 2005-02-03 12:03:48 re: a function for g(x) Federico Kereki 2005-02-03 12:01:56 a function for F(x), for G(x) Infiniti 2005-02-03 08:17:07 a function for f(x) suman 2005-02-02 22:15:09 a function for g(x) suman 2005-02-02 22:11:10 a g(x) [piecewise] Jer 2005-02-02 20:09:42 solution (spoiler) Charlie 2005-02-02 19:38:43 Some f(x)'s Jer 2005-02-02 18:50:23

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