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Math Help - Prove function is strictly decreasing

  1. #1
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    Prove function is strictly decreasing

    I've got functions  f,g:\mathbb{R}\rightarrow \mathbb{R} .  f is strictly increasing and  f\circ g is strictly decreasing I am asked to show  g is strictly decreasing. I already have a solution in front of me however I would like to know if this approach is correct.

    Suppose x_{1} < x_{2} then f\left ( g\left ( x_{1} \right ) \right ) > f\left ( g\left ( x_{2} \right ) \right )   \Rightarrow  g\left ( x_{1} \right ) > g\left ( x_{2} \right ) since  f is strictly increasing.

    therefore  g is strictly decreasing.
    Last edited by theintervurt; November 20th 2012 at 08:10 AM.
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  2. #2
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    Re: Prove function is strictly decreasing

    Yes, that's good.
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