# Increasing function

• April 5th 2011, 09:13 PM
Hardwork
Increasing function
Ok, I've a question. For a certain function f(x), it's been shown:

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

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

$f(x) \to +\infty$ when $x \to +\infty$.
• April 5th 2011, 11:27 PM
CaptainBlack
Quote:

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

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

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

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

For any real $r>0,\ f(x)>r$ for all $x>2^{2r}$.

That is $f(x)$ is bigger than any given real for $x$ sufficiently large

CB