On Jan 22, 11:37 am, David C. Ullrich <dullr...@sprynet.com> wrote: > On Wed, 21 Jan 2009 14:48:10 EST, amy666 <tommy1...@hotmail.com> > wrote: > > >btw all "math" on denis website is actually stolen and copied from others. > > >tell me something , if c = positive real and > > >f(ax)=(f(x))^2+b > > >then what is > > >f(a^c x) = ?? > > Why in the world do you imagine that f(ax)=(f(x))^2+b > implies anything about f(a^c x) (when c is not an integer)? > > Supposing it did imply something about that, why would > you imagine that this has something to do with continuuous > iteration?
The connection with continuous iteration is like this...
Assume f(1) = k and define g(x) = x^2 + b, then
f(a^n) = g^n(k)
f(x) = g^(log(x)/log(a))(k)
So if we can find an expression for g^n(x) for arbitrary real n then we have a solution for f(x).