Let $f$ be an entire function such that $\lvert f\rvert$ approaches infinity as $\lvert z\rvert$ tends to infinity. Then
- $f(1/z)$ has an essential singularity at $0$.
- $f$ cannot be a polynomial.
- $f$ has finitely many zeros.
- $f(1/z)$ has a pole at $0$.
Option 2 is false, what about 1, 3, 4?