
Bounded polynomials.
Hi,
if $\displaystyle f(z)$ is a polynomial with $\displaystyle z$ a complex number. Then, is it always true that if the domain of $\displaystyle f$ is bounded then $\displaystyle f$ must be a bounded function?
Also, is it aways true that as we increase $\displaystyle z$ we see that $\displaystyle f(z)$ increase also? I think this must be the case as polynomials only admit non negative powers.
any help or clarification would be appreciate!
Thanks

Re: Bounded polynomials.
1. Yes. f(z) = an z^n +...+ a0  <= anz^n + ... + a0
2. When z is big enough this is true. While if z is relatively small consider the example f(z)=1z. f(1)=0<1=f(0)