Image
The image of a function \(f:X \rightarrow Y\) is defined to be the set \(f(X)\) of all \(f(x) \in Y\), given \(x \in X\). That is:
\[ f(X)=\{ f(x) : x \in X \} \] (sidenote: We remark that the image of a function is always a subset of the codomain of \(f\). That is: \(f(X) \subseteq Y\) )