Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "Range"

m
 
Line 9: Line 9:
  
 
[[Category:Definition]]
 
[[Category:Definition]]
 +
{{stub}}

Latest revision as of 19:15, 3 February 2016

Let $A$ and $B$ be any sets and let $f:A\to B$ be any function between them, so that $A$ is the domain of $f$ and $B$ is the codomain. Then $\{b\in B\mid \mathrm{there\ is\ some\ } a\in A\mathrm{\ such\ that\ } f(a)=b\}$ is called the range or image of $f$.

Thus, if we have $f: \mathbb{R} \to \mathbb{R}$ given by $f(x) = x^2$, the range of $f$ is the set of nonnegative real numbers.

A function is a surjection exactly when the range is equal to the codomain.

See also

This article is a stub. Help us out by expanding it.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Range&oldid=75157"