Suppose we have say $f(2x)=\left(f(x)\right)^4,$ with $f(0)=1$ and $f$ not being constant. How does one find out what $f$ is without guessing?
More generally, is there a systematic way of finding non-obvious functions that solve $f(x)=g(f(h(x)))?$
Suppose we have say $f(2x)=\left(f(x)\right)^4,$ with $f(0)=1$ and $f$ not being constant. How does one find out what $f$ is without guessing?
More generally, is there a systematic way of finding non-obvious functions that solve $f(x)=g(f(h(x)))?$