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Math Help - Prove a function is bounded

  1. #1
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    Prove a function is bounded

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

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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Yes!
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  3. #3
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    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.
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  4. #4
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    Ok, thank you, i'll do that!
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  5. #5
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by Ackbeet View Post
    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!
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  6. #6
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    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 (0, \infty) other than 1.
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