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Surjective proof & finding inverse

  1. Nov 10, 2013 #1
    prove the function ## g: \mathbb{N} \rightarrow \mathbb{N} ## ## g(x) = \left[\dfrac{3x+1}{3} \right] ## where ## [y] ## is the maximum integer part of r belonging to integers s.t. r less than or equal to y is surjective and find it's inverse

    I know this function is bijective, but how do I prove it's surjective? Could I just say g(x) = y ## \left[\dfrac{3x+1}{3} \right] = y ## so ## x = \left[\dfrac{3y-1}{3} \right ] ## and say that ## g^{-1}(x) = \left[\dfrac{3y-1}{3} \right ] ##
     
  2. jcsd
  3. Nov 10, 2013 #2

    FeDeX_LaTeX

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    Gold Member

    Yikes, talk about last-minute.

    It may help you to split up that fraction.
     
  4. Nov 11, 2013 #3
    last-minute what?
     
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