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Math Help - increasing functions prove strictly increasing

  1. #1
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    increasing functions prove strictly increasing

    Prove: If f and g are increasing functions on an interval I and I is a subset of R, reals . Show that f+g is an increasing function on I. If f is also strictly increasing on I, then f+g is strictly increasing on I.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by apple2010 View Post
    Prove: If f and g are increasing functions on an interval I and I is a subset of R, reals . Show that f+g is an increasing function on I. If f is also strictly increasing on I, then f+g is strictly increasing on I.
    This is not very hard friend.

    If x\leqslant y then f(x)\leqslant f(y),g(x)\leqslant g(y) so....
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  3. #3
    Junior Member NowIsForever's Avatar
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    If x ≤ y, then f(x) ≤ f(y) and g(x) ≤ g(y), so (f+g)(x) = f(x) + g(x) ≤ f(y) + g(y) = (f+g)(y)

    If x < y, then f(x) < f(y) and g(x) ≤ g(y), so (f+g)(x) = f(x) + g(x) < f(y) + g(y) = (f+g)(y)
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