One to One (Injective) function

A function f: X → Y is said to be a one-to-one function if the images of distinct elements of X under f are distinct. Thus, f is one to one if f(x1) = f(x2)

Property: A function f: A → B is one-to-one if f(x1) = f(x2) implies x1 = x2, i.e, an image of a distinct element of A under f mapping (function) is distinct.

Condition to be One-to-One function: Every element of the domain has a single image with a codomain after mapping.

Read More about One-to-One Functions.

Examples of One to One Functions

Som of examples of one-one functions are:

  • f(x) = x (Identity function)
  • k(x) = 2x + 3 (Linear Polynomial)
  • g(x) = ex (Exponential function)
  • h(x) = √x​ (Square root function, defined for x ≥ 0)

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

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What is a Function?

A function is a relation between two sets set A and set B. Such that every element of set A has an image in set B and no element in set A has more than one image in set B....

Types of Functions in Maths

An example of a simple function is f(x) = x3. In this function, f(x) takes the value of “x” and then cubes it to find the value of the function. For example, if the value of x is taken to be 2, then the function gives 8 as output i.e. f(2) = 8....

One to One (Injective) function

A function f: X → Y is said to be a one-to-one function if the images of distinct elements of X under f are distinct. Thus, f is one to one if f(x1) = f(x2)...

Many to One Function

If the function is not one to one function, then it should be many to one function means every element of the domain has more than one image at codomain after mapping....

Onto (Surjective) Function

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Into Function

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Summary: Types of Functions

All types can be summarized in the following table:...

Solved Examples on Types of Function

Example 1: Check whether the function f(x) = 2x + 3, is one-to-one or not if Domain = {1, 2, 1/2} and Codomain = {5, 7, 4}...

FAQs on Types of Function

What is domain and codomain of a function?...