# Example 39 - Chapter 1 Class 12 Relation and Functions

Last updated at June 29, 2018 by Teachoo

Last updated at June 29, 2018 by Teachoo

Transcript

Example 39 Show that – a is the inverse of a for the addition operation ‘+’ on R and 1a is the inverse of a ≠ 0 for the multiplication operation ‘×’ on R. Addition An element a in R is invertible if, there is an element b in R such that , a * b = e = b * a Here, b is the inverse of a Here, e = 0 for addition So, a * b = e = b * a a + b = 0 = b + a ⇒ b = –a Since a + (– a) = 0 = (– a) + a = 0, So, –a is the inverse of a for addition. Multiplication An element a in R is invertible if, there is an element b in R such that , a * b = e = b * a Here, b is the inverse of a Here, e = 1 for multiplication So, a * b = e = b * a a × b = 1 = b × a ⇒ b = 1𝑎 Since a × 1𝑎 = 1 = 1𝑎 × a So, 𝟏𝒂 is the inverse of a for addition.

Examples

Example 1

Example 2

Example 3

Example 4 Important

Example 5

Example 6 Important

Example 7

Example 8

Example 9

Example 10

Example 11 Important

Example 12 Important

Example 13 Important

Example 14 Important

Example 15

Example 16

Example 17

Example 18 Important

Example 19 Important

Example 20

Example 21

Example 22

Example 23 Important

Example 24

Example 25 Important

Example 26

Example 27 Important

Example 28

Example 29

Example 30

Example 31

Example 32

Example 33

Example 34

Example 35

Example 36

Example 37

Example 38

Example 39 You are here

Example 40

Example 41 Important

Example 42 Important

Example 43 Important

Example 44

Example 45 Important

Example 46 Important

Example 47 Important

Example 48 Important

Example 49

Example 50

Example 51 Important

Chapter 1 Class 12 Relation and Functions

Serial order wise

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.