Consider a non-univalent analytic function $f: U \to \mathbb{C}$. Such a function does not have an inverse function, which would mean, as we recall , a function $g: f(U) \to U$ satisfying $g\left[ f(z) \right] = z$ for every $z$ in $U$ and $f(\left[ g(z) \right]=z$ for all $z$ in $f(U)$. What $f$ does have- and has in abundance are so called right inverse functions. This name is attached to any function $g: f(U) \to U$ enjoying the only latter property, $ f \left[ g(z) \right]=z$ for every $z$ in $U$
Page-85, Bruce P. Palka
Could someone explain why a complex function has right inverses but not left inverses? Maybe an explanation with an explicit example would help.