---
tag: J5DEEKRRCY
kind: concept
name: Image (mathematics)
aliases: [function-image, image-function, image-functions, image-of, pre-image, preimage]
sources:
  - wikipedia: en:579311@r1360048754
    locator: Image (mathematics)
    note: adopted
    mention: wikipedia://en/579311
    sections: [Summary]
same_as:
  wikidata: Q860623
  wikipedia: Image (mathematics)
inventory: [T560Q70Q45]
---

## Summary

In mathematics, the **image** of a [[function|0EPAT51DXQ]] $f: X \to Y$ is the [[set|0BSJ7RQ9BW]] of all $f(x)$ such that $x$ belongs to the [[domain|0Q4CBD3HX0]] 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|0NF1KGDXX3]] of $f$ to $S$.