Ok, I've a question. For a certain function f(x), it's been shown:

If $\displaystyle x > 2^k$ then $\displaystyle f(x) > f(2^k) > \frac{1}{2}k$.

Fine. My question is the following: how does it follow that:

$\displaystyle f(x) \to +\infty$ when $\displaystyle x \to +\infty$.