Check sibling questions

f: A -> B

A relation from A to B is a function if every element of set A has one and only one image in set B.

 

∴ For a function

  1. Every element of set A will have an image.
  2. Every element of set A will only one image in set B

Let us take an example

Let A = {a, b, c, d}

and B = {Aman, Ankit, Baljinder, Chandu, Eklavya}

 

Check if the following are functions?

Function - Example 1.jpg

-a-

For a function

  1. Every element of set A will have an image.
  2. Every element of set A will only one image in set B

 

Since d doesn’t have a image,

it is not a function

-ea-

Functions - Part 2

-a-

For a function

  1. Every element of set A will have an image.
  2. Every element of set A will only one image in set B

 

Since a has two images,

it is not a function

-ea-

Functions - Part 3

-a-

For a function

  1. Every element of set A will have an image.
  2. Every element of set A will only one image in set B

 

Since every element has an image,

and every element has only one image.

Hence, it is a function

 

So, the function is

f = {(a, Aman), (b, Baljinder), (c, Chandu), (d, Eklavya)}

 

Domain = Set of first elements = {a, b, c, d}

Range = Set of second elements = {Aman, Baljinder, Chandu, Eklavya}

Codomain = Second set = {Aman, Ankit, Baljinder, Chandu, Eklavya}

-ea-

Note : In a function, domain will always be equal to first set.


Functions - Part 4

-a-

For a function

  1. Every element of set A will have an image.
  2. Every element of set A will only one image in set B

 

Since every element has an image,

and every element has only one image.

Hence, it is a function

 

So, the function is

f = {(a, Ankit), (b, Baljinder), (c, Chandu), (d, Eklavya)}

 

Domain = Set of first elements = {a, b, c, d}

Range = Set of second elements = {Ankit, Baljinder, Chandu, Eklavya}

Codomain = Second set = {Aman, Ankit, Baljinder, Chandu, Eklavya}

-ea-

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.