Are the following either one-to-one or onto functions?

Question

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?

Answer 1

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.