Mapping/Preimage under a mapping/Definition

Preimage of a set

Let ${}L$ and ${}M$ be sets, and let

$F\colon L\longrightarrow M$

be a mapping. For a subset ${}T\subseteq M$, we call

${}F^{-1}(T)={\left\{x\in L\mid F(x)\in T\right\}}\,$

the preimage of ${}T$ under ${}F$. For a subset ${}T=\{y\}$ with one element, we call

$F^{-1}(\{y\})$

also the preimage of ${}y$.