Thread: Prove a function is bounded

Is this enough to prove that g(x) is bounded?

Yes!

I would disagree, because you don't know what's happening in-between zero and infinity. If you show that g is monotonically decreasing, you'd have shown what you need to show.

Ok, thank you, i'll do that!

Originally Posted by Ackbeet

I would disagree, because you don't know what's happening in-between zero and infinity. If you show that g is monotonically decreasing, you'd have shown what you need to show.

But it's obvious!

Yes, it is obvious but it still needs to be said to have a complete proof. What Utherr showed in his first post was that this function is continuous at x= 1. Now he only needs to observe that f(x) is a composition of bounded functions for all x in other than 1.