Image (functions)

Image of $f$ is a subset of $f$‘s codomain that is output of $f$ on a subset of its domain (image is the smaller oval inside $Y$).

• Image of $x\in X$ under $f$ is $f(x)=y$ (value of $f$ when applied to $x$)
• Image of a subset $A\subseteq X$ under $f$ is subset $f[A]\subseteq Y$ defined by $f[A]=\{y\in Y|y=f(x)\text{ for some }x\in A\}$
• Image $f[X]$ of entire domain $X$ of $f$ is called the image of $f$.