Increasing function

**Hardwork** · April 5th 2011, 08:13 PM

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 $x \to +\infty$ .

**CaptainBlack** · April 5th 2011, 10:27 PM

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

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