Let $f(z) = f(z^2)$, for all $z\in\mathbb{D}$ with $f(1) = 1$, then which of the following is incorrect?
Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,