Inverse image

Inverse image

Let ${\displaystyle f}$ be a function from ${\displaystyle X}$ to ${\displaystyle Y.}$ The preimage or inverse image of a set ${\displaystyle B\subseteq Y}$ under ${\displaystyle f,}$ denoted by ${\displaystyle f^{-1}[B],}$ is the subset of ${\displaystyle X}$ defined by $${\displaystyle f^{-1}[B]=\{x\in X\,:\,f(x)\in B\}.}$$