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Inverse super-composition
Okey, I have found something looking like the solution. I feel I am closer than ever before.
For the following functional equation

my method gives:
Let us check it:
looks like sg like the exoponential function.

Of course, because at x=0 exp x = 1, then x2^n will never go up to 1, so in the reals there is no more beautiful solution for N like mine, I think or I am wrong, ain't I?

What do you think, is this function correct? Or is there better?
Xorter Unizo
Hi here, again!

I have been thinking about functional logarithm, and I coded it in pari/gp in this way:


M is the Carleman-matrix, T is a generated taylor-series from the M matrix. Ln is log of a quadratic matrix. And olog is the functional logarithm: olog(f(x),(f^og(x))(x)) = g(x), but somewhy it is not working.
E. g. olog(2x,x*2^(2x),100...) = 2x.
Could help me?
Thank you very much!
Xorter Unizo

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