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I just want to see if i'm on the right path in determining if the following are onto or one to one.

$f\circ g = 3 \lfloor (x+1)/2 \rfloor$

$g\circ f = \lfloor (3x+1)/2 \rfloor$

Both functions are from set of integers to set of integers.

Neither of these is onto or one-to-one. Am I correct?

Mandeyo
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    What is supposed to be onto/one-to-one? Is it $f$? Is it $g$? Or their compositions? And you're forgetting an important part of these properties, if we let $f,g : \mathbb{N} \to \mathbb{C}$, then of course, these are not onto. Do you see what I mean? – Qi Zhu Mar 18 '18 at 21:26
  • Yes sorry they are both from set of integers to set of integers. – Mandeyo Mar 18 '18 at 21:29

1 Answers1

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You are correct.

Let us call the first one F and the second one G. The ranges are just integers so none of them is onto. For the first one $F(0)=F(1/2) = 0$ so it is not one-to-one.

For the second one $G(0)=G(1/4)=0$ so it is not one-to- one.

Mohammad Riazi-Kermani
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