Preimage of a Function

• Definition: For $F:A\to B$ and $Y\subseteq B$, the preimage of $Y$ is the Set of all $x\in A$ that map into $Y$.
• Formally: $f^{-1}(Y)=\{x\in A\mid f(x)\in Y\}$
• Note: “Preimage of y” means all $x$ that map to that single $y$.
• Example: If $f(x)=x^2$, the preimage of 9 is $\{-3,3\}$.