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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 f(x) Comment 12 of 12 |
f(x)=n-x for any number n works because f(f(x))=n-(n-x)=x.

 Posted by Math Man on 2013-05-14 12:22:27
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