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Math Help - If f and g are real functions and (f+g)(x) is bounded above...

  1. #1
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    If f and g are real functions and (f+g)(x) is bounded above...

    Prove that both f and g are bounded above.
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  2. #2
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    Quote Originally Posted by Mitchell View Post
    Prove that both f and g are bounded above.
    Let f,g:\mathbb{R} \to \mathbb{R} : f(x) = x, \ g(x) = -x

    Then, (f+g)(x) = x + (-x) = 0 \Rightarrow (f+g)(x) is bounded above by M = 0

    But f(x) definitely is not bounded above...
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  3. #3
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    The other direction is true, however.
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