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Thread: Is inverse function increasing?

  1. #1
    Aug 2010

    Is inverse function increasing?

    If f(x) increasing, f(x) > 0.
    dy=f(x)dx, dx/dy=1/f(x) > 0.

    Therefore inverse function is increasing.

    Given, if a>b, f(a)>f(b)

    assume f(a)<f(b) but a>b. a>b → f(a)>f(b). Therefore b>a.
    therefore, if f(a) > f(b), a>b

    ie, inverse function is also increasing

    shortened version from wicki-
    Inverse of increasing function is increasing - Calculus

    (Seems obvious now but never occurred to me.)
    Last edited by Hartlw; Oct 4th 2013 at 06:56 AM. Reason: alternate proof
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