非有理函数与有理函数的复合可以是有理的吗？

hbghlyj

math.stackexchange.com/questions/2762019/can- … ational?noredirect=1

Suppose $f(z)$ is continuous and surjective onto $\Bbb C$, but not rational. Let $R$ and $Q$ be non-constant rational functions. Can we have $R(f(z))=Q(z)$?

例如$R(z)=\frac1{1-z^2},Q(z)=\frac1{1-z}$和$f(z)=\sqrt z$

hbghlyj

在$\mathbb R$上有定义且不单调的有理函数