Does inverse of a nontrivial holomorphic function always have a branch point?

Does inverse of a nontrivial holomorphic function always have a branch point?

pAny nontrivial (i.e. which is not a first order polynomial) entire in
$\mathbb{C}$ function I have thought of has a multifunction as its inverse
and has a branch point. For example, $x^n\to\sqrt[n]{x}$, $\exp(x)\to\ln
x$, etc./p pSo I have a question: are there any nontrivial entire
functions, inverses of which have no branch points?/p