Given a positive integrer number $n$ ($n\ne 0$), let $f(n)$ be the average of all the positive divisors of $n$. For example, $f(3)=\frac{1+3}{2}=2$, and $f(12)=\frac{1+2+3+4+6+12}{6}=\frac{14}{3}$.

[b]a[/b] Prove that $\frac{n+1}{2} \ge f(n)\ge \sqrt{n}$.

[b]b[/b] Find all $n$ such that $f(n)=\frac{91}{9}$.