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Last updated at Jan. 28, 2020 by Teachoo

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Ex 1.2, 5 Show that the Signum Function f: R โ R, given by f(x) = {โ(1 for ๐ฅ >0@ 0 for ๐ฅ=0@โ1 for ๐ฅ<0)โค is neither one-one nor onto. f(x) = {โ(1 for ๐ฅ >0@ 0 for ๐ฅ=0@โ1 for ๐ฅ<0)โค For example: f(0) = 0 f(-1) = โ1 f(1) = 1 f(2) = 1 f(3) = 1 Since, different elements 1,2,3 have the same image 1 , โด f is not one-one. Check onto f: R โ R f(x) = {โ(1 for ๐ฅ >0@ 0 for ๐ฅ=0@โ1 for ๐ฅ<0)โค Value of f(x) is defined only if x is 1, 0, โ1 For other real numbers(eg: y = 2, y = 100) there is no corresponding element x Hence f is not onto Thus, f is neither one-one nor 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

Example 9

Example 11 Important

Misc 5

Ex 1.2, 5 Important You are here

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.