When discussing functions, we have notation for talking about an element of the domain (say \(x\)) and its corresponding element in the codomain (we write \(f(x)\text{,}\) which is the image of \(x\)). Sometimes we will want to talk about all the elements that are images of some subset of the domain. It would also be nice to start with some element of the codomain (say \(y\)) and talk about which element or elements (if any) from the domain it is the image of. We could write “those \(x\) in the domain such that \(f(x) = y\text{,}\)” but this is a lot of writing. Here is some notation to make our lives easier.
in-context