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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)

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Some f(x)'s | Comment 1 of 12

f(x) = 1/x

f(x) = -1/x

f(x) = 1/(x-a) + a for any a

f(x) = 1/(a-x) + a for any a

f(x) = a-x for any a

These are just functions symmetric across the identity line.


  Posted by Jer on 2005-02-02 18:50:23
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