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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 ] ##
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 ] ##