Onto (Surjective) Function
A function f: X → Y is said to be an onto function if every element of Y is an image of some element of set X under f, i.e for every y ∈ Y there exists an element x in X such that f(x) = y.
Properties:
- The range of functions should be equal to the codomain.
- Every element of B is the image of some element of A.
Condition to be onto function: The range of function should be equal to the codomain.
As we see in the above two images, the range is equal to the codomain means that every element of the codomain is mapped with the element of the domain, as we know that elements that are mapped in the codomain are known as the range. So these are examples of the Onto function.
Read More about Onto Functions.
Examples of Onto Functions
Some of the most common examples of onto functions are:
- f(x) = x (Identity function)
- g(x) = ex (Exponential function)
- h(x) = sin(x) (Sine function within a limited domain, e.g., h : R→[−1,1])
- k(x) = cos(x) (Cosine function within a limited domain, e.g., k : [0,π]→[−1,1])
- m(x) = x3 (Cubic function)
Types of Functions
Functions are defined as the relations which give a particular output for a particular input value. A function has a domain and codomain (range). f(x) usually denotes a function where x is the input of the function. In general, a function is written as y = f(x).
Table of Content
- What is a Function?
- Types of Functions in Maths
- One to One (Injective) function
- Many to One function
- Onto (Surjective) Function
- Into Function
- Summary: Types of Functions