$f(z)$ be an entire function such that $|zf(z)-1+e^z| \leq 1+|z| \forall z \in \mathbb{C}$ then what can we say about such function value at $z=0$ and its derivative at $z=0$?
I know the basic definition of entire functions and their properties but am still confused about how to approach this problem.
Any hint is appreciated