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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: ( You must be logged in to post comments.)
  Subject Author Date
Solutionf(x)Math Man2013-05-14 12:22:27
re: a working function fore f(x)Dimmeh2005-08-22 10:35:48
Here's an infinte number of f(x) that all work!!!Dimmeh2005-08-22 10:35:09
a working function fore f(x)mates catalin2005-02-26 12:06:18
Some Thoughtsre: a function for F(x), for G(x)Federico Kereki2005-02-03 12:03:48
Some Thoughtsre: a function for g(x)Federico Kereki2005-02-03 12:01:56
a function for F(x), for G(x)Infiniti2005-02-03 08:17:07
Solutiona function for f(x)suman2005-02-02 22:15:09
Solutiona function for g(x)suman2005-02-02 22:11:10
a g(x) [piecewise]Jer2005-02-02 20:09:42
Solutionsolution (spoiler)Charlie2005-02-02 19:38:43
Some f(x)'sJer2005-02-02 18:50:23
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