I am not familiar with the notion "characterize" in the following context. Does this mean to redefine or?.... Any help would be appreciated. Thank you.
For a function $f:X\to Y$, and y an element of Y, let $f^{-1}(y) := \{ x \in X| f(x) = y\}$. This is sometimes called the "fibre" of f over y.
Problem: characterize 1 to 1 and onto functions in terrm of the fibres