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Last updated at May 29, 2018 by Teachoo

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Example 8 Show that the function f : N N, given by f (x) = 2x, is one-one but not onto. Given, f(x) = 2x One-One f (x1) = 2x1 f (x2) = 2x2 Putting f(x1) = f(x2) 2x1 = 2 x2 x1 = x2. Hence, if f(x1) = f(x2) , x1 = x2 function f is one-one Onto f(x) = 2x Let f(x) = y , such that y N 2x = y x = 2 If y = 1 x = 1 2 = 0.5 , which is not possible as x N Hence, f is not onto

To prove one-one & onto (injective, surjective, bijective)

One One function

Onto function

One One and Onto functions (Bijective functions)

Example 7

Example 8 You are here

Example 9

Example 11 Important

Misc 5

Ex 1.2, 5 Important

Ex 1.2 , 6

Example 10

Ex 1.2, 1

Ex 1.2, 12

Ex 1.2 , 2 Important

Ex 1.2 , 7

Ex 1.2 , 11

Example 12 Important

Ex 1.2 , 9

Ex 1.2 , 3

Ex 1.2 , 4

Example 50

Example 51 Important

Ex 1.2 , 10 Important

Misc. 4 Important

Example 13 Important

Example 14 Important

Ex 1.2 , 8 Important

Example 46 Important

Misc 10 Important

Chapter 1 Class 12 Relation and Functions

Concept wise

- Relations - Definition
- Empty and Universal Relation
- To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
- Function - Definition
- To prove one-one & onto (injective, surjective, bijective)
- Composite functions
- Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.