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Math Help - Bounded functions ..

  1. #1
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    Bounded functions ..

    Hello
    small question:

    if f and g are bounded function then so is f+g and f-g

    but what about fg and f/g ?
    Are they will be bounded also?
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  2. #2
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    If you know that |f(x)| <= C and |g(x)| <= C, then it is easy to find an upper bound on |f(x) * g(x)|.

    On the other hand, f(x) / g(x) can be very large even if |g(x)| <= 1. In fact, in this case |f(x) / g(x)| can be made arbitrarily large by keeping f(x) constant and changing g(x) a little (by no more than 1).
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  3. #3
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    Quote Originally Posted by Liverpool View Post
    Hello
    small question:

    if f and g are bounded function then so is f+g and f-g

    but what about fg and f/g ?
    Are they will be bounded also?

    If f is bounded by M, and g is bounded by N, then certainly it's true that fg is bounded by MN.

    For f/g: what if g → 0 somewhere in its domain, and f = 1 at that same location?
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  4. #4
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    Thanks!
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