Image (mathematics)

Summary

In mathematics, the image of a function $f: X \to Y$ is the set of all $f(x)$ such that $x$ belongs to the domain of $f$. The image by $f$ of an element $x$ of the domain of $f$ is $f(x)$, that is, the output corresponding to the input $x$. The image by $f$ of a subset $S$ of the domain of $f$ is the set of all $f(x)$ such that $x$ is in $S$, that is, the set of the images of the elements of $S$. Equivalently, it is the image of the restriction of $f$ to $S$.