Suppose you have: $$f:\Bbb R \rightarrow\Bbb Z \text{ where } f(x)= \lceil 2x-1 \rceil$$
Well, I know that this is not a one-to-one function, but I don't know how to show that it's onto. The reason being the ceiling constraints. What I thought of was: $$ f(x)= \lceil 2x-1 \rceil = \lceil 2x \rceil -1 \\ f(x)=y\\y+1 = \rceil = \lceil 2x \rceil $$
But I don't know what to do past this point.