We can do this in the other direction as well. We might ask which elements of the domain get mapped to a particular set in the codomain. Let \(f:X \to Y\) be a function and suppose \(B \subseteq Y\) is a subset of the codomain. Then we will write \(f\inv(B)\) for the inverse image of \(B\) under \(f\), namely the set of elements in \(X\) whose image are elements in \(B\text{.}\) In other words, \(f\inv(B) = \{x \in X \st f(x) \in B\}\text{.}\)
in-context