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Function(Function()) Finding (Posted on 2005-02-02) Difficulty: 5 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: a function for F(x), for G(x) | Comment 8 of 12 |
(In reply to a function for F(x), for G(x) by Infiniti)

I don't think G(x) works: G(G(0.5))= G(log(0.5)), which is undefined since log(0.5)<0.
  Posted by Federico Kereki on 2005-02-03 12:03:48

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