Set theoretic definition of pre-image – math.stackexchange.com
Jacob Lockard
Let $f : X \to Y$ and let $B \subseteq Y$. Then according to Wikipedia, the preimage of $B$ under $f$ is defined like
\begin{align*}
f^{-1}\bigl[B\bigr] = \bigl\{ x \in X \;:\, f(x) \in B \bigr\} ...