Now I just have the equation $f(f(x))=x^2+x$. How can I find $f(x)$?
I have already tried many times, but I cannot solve it by any way I know. Is a solution possible?
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2Maybe you should start with reading this old post: http://mathoverflow.net/questions/17614/solving-ffx-gx?rq=1 – Joonas Ilmavirta Aug 26 '14 at 17:38
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Domain? Continuity requirements? – Robert Israel Aug 26 '14 at 18:29
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4The post cited as duplicate is barely relevant. Much better is this: http://math.stackexchange.com/q/208996/442 – Gerald Edgar Aug 26 '14 at 18:39
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1If it were $f(f(x))=x^2+2x$ then the solution would be $f(x)=(1+x)^{\sqrt{2}}-1$ For your function the closed-form solution may be not existing. – Anixx Sep 14 '14 at 18:12