> [!NOTE] **Definition** (Image) > Suppose $X$ and $Y$ are sets. Suppose that $f:X\to Y$ is a [[Function|function]]. For any $A \subset X$ its image under $f$ is given by $f(A)=\{ f(x)\mid x\in A \} = \{ y \in Y\mid \exists x\in A \; \text{ s.t. } \; f(x) =Y \}.$ # Applications See application [[Image of Homomorphism of Groups]] See [[Continuous Image of an Interval is an Interval]].