Hello everyone I was wondering if anyone could give me a hand with this

Let f be an entire function such that $\displaystyle |f(z)| \rightarrow \infty $as |$\displaystyle z| \rightarrow \infty$. Define g by

$\displaystyle

g(z)=f(1/z) $

where $\displaystyle (z \not= 0)

$

Show that g has a pole at 0, and, by considering the Laurent series for g about 0, show that f is a polynomial function.

Im not so worried about the 2nd part yet but i was wondering how to show that g has a pole, intuitvely i can see that it has one at zero

i am trrying to express g as

$\displaystyle g(z) = \frac{h(z)}{z}$ where h(z) is analytic on some open disc around 0 and $\displaystyle k(0) \not= 0$

but im not sure how to do this

any help would be appreciated, thank you