Preimage

Definition

Let $f$ be a function from $X$ to $Y$. The preimage of a set $B \subseteq Y$ under $f$, denoted by $f^{- 1}\left. (B) \right.$ is the subset of $X$ defined by

$$ f^{- 1}\left. (B) \right. = \{ x \in X:f\left. (x) \right. \in B\} $$

Examples

For the function $f\left. (x) \right. = x^{2}$, the preimage of $\{ 4\}$ would be $\{ - 2,2\}$.