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    ben.prez's Avatar
    ben.prez Posts: 1, Reputation: 1
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    #1

    Mar 16, 2010, 10:00 AM
    show that f is increasing if and only if the function g = 1/f is decreasing
    This question involves formal proof and set theory, as well as a knowledge of functions.
    takeonme's Avatar
    takeonme Posts: 5, Reputation: 1
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    #2

    May 4, 2010, 03:33 PM

    Suppose f is increasing. Then for all h>0, f(x+h)>f(x). Then by rules of inequalities, 1/f(x+h) < 1/f(x). So g(x+h)<g(x) where g=1/f. Hence g is decreasing.

    Proof can be reversed to get iff.
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