Trying to solve f(f(x)) = x**2 - 2

Problem: Find satisfying the functional equation

First, let us note that the equation

has simple solutions

One can try to reduce (1) to (2) by changing "coordinates" with

In y coordinates, eq.(1) can be written down as
where

Requiring eq.(2) for gives

or
or
where we denoted
Now a solution g(y) of the new functional equation (9) will transform a solution (3) of eq.(2) (more precisely, the solution of the eq.(7)) into a solution of eq.(1):


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Topic revision: r1 - 2012-03-10 - AlexanderFedotov
 
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