Function Terminology

A function is a relation between a set of inputs (called the domain), and a permissible set of outputs (called the codomain), such that each input is is related to exactly one output. We often denote a function on 1 variable by \( f\). When \( x\) is an element of the domain, we say that the output has the value \( f(x)\).

We can certainly add irrelevant items to the codomain, like {alligator}, {purple} and {Brilliant}. As such, we define the range of a function (also called the image) to be the set of all attained outputs. Note that by definition, the range of a function has to be a subset of the codomain.

Here are a few more terms that it is helpful to know:

  • Injective: An injective function is one that maps every value in the domain to a unique value in the codomain, such that for any given value in the range there is only one corresponding value in the domain. Injective functions are also called "one-to-one" functions.
  • Surjective A surjective function is one that covers every element in the co-domain, such that there are no elements in the co-domain that are not a value of the function. In a surjective function the range and the codomain will be identical.
  • Bijective A bijective function is both injective and surjective.

Note by Arron Kau
4 years, 4 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link]( link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)


There are no comments in this discussion.


Problem Loading...

Note Loading...

Set Loading...