Let $f(z)=\sum_{n\ge1}a_nz^n$ be a power series of $\mathbb C_p[[z]]$ where the $a_n$ are such that $|a_n|=1$ for every positive integer $n$. Consider $z_0\in\mathbb C_p$ such that $|z_0|<1$. Can one assert that there exist $x_0\in \mathbb C_p$ with $|x_0|<1$ such that $f(x_0)=z_0$.



Thanks in advance for any answer.