find all entire functions that are 1-1 That is all the given information.
I should find all the entire functions that are one to one, I have no clue on how to do that.
And there is also another one, that goes like this:
Find all entire functions that are:
$$\forall z \in \mathbb C^* \;\;\;\;\; \lvert f(z)\rvert \le \lvert \frac{\sin z}{z} \rvert$$
$$\mathbb{C}^* \text{ is complex plane without } (0,0)$$

Hint: Observe that if a function $f$ is entire and one to one, then $f$ cannot have an essential singularity at $\infty$ by the great Picard's theorem. This means the Taylor series expension of $f$ at $0$ has only finitely many terms, and thus $f$ is a polynomial. Now note that a polynomial is one-to-one if and only if the degree is $1$.
