Find all real monotone fcns f such that f(f(x)) = f(x) + 2x  TOPIC_SOLVED

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Find all real monotone fcns f such that f(f(x)) = f(x) + 2x

Postby james_bond on Sun May 17, 2009 4:13 pm

is a real, monotonous function and for all real : . The task is to find all the functions with this property. I have succeeded in showing that the function is strictly monotonous, and trying the linear functions found that only and are solutions and therefore I guess that there are no other solutions but I can't prove it. Any help would be greatly appreciated.
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Postby stapel_eliz on Mon May 18, 2009 4:43 pm

I couldn't get much further than you did, but other could; for instance, try here. :blush:

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