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Is $f:\mathbb{R}^2\to\mathbb{R}^2$ given by $f(x,y)=(2x+y,3\lfloor y\rfloor-x)$ bijective? if not is it injective or surjective?

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Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. If this is homework, please add the homework tag; people will still help, so don't worry. – Julian Kuelshammer Nov 3 '12 at 15:08
What is the domain of this function? What is the range? – Asaf Karagila Nov 3 '12 at 15:08
Write out what it would mean if there were two points mapped to the same point. Examine the range of the function. If you get stuck in this routine verification, you can always show us where you get stuck. – rschwieb Nov 3 '12 at 15:25
it is from RxR to RxR and I finally managed to solve it and I found f-1(x,y) ...5 pages of proof :| a really beautiful problem that is – myself Nov 3 '12 at 17:58
If you want, you can write up your solution here as an answer and eventually accept it; this is not only acceptable but encouraged. (You have to wait some interval after posting the answer before you can accept it; I forget how long it is, but it’s at least several hours.) – Brian M. Scott Nov 3 '12 at 21:22

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