Example 13 - Chapter 1 Class 12 Relation and Functions
Last updated at May 29, 2018 by Teachoo
Transcript
Example 13 (Method 1) Show that an onto function f : {1, 2, 3} {1, 2, 3} is always one-one. Since f is onto, all elements of {1, 2, 3} have unique pre-image. Following cases are possible Since every element 1,2,3 has either of image 1,2,3 and that image is unique f is one-one Example 13 (Method 2) Show that an onto function f : {1, 2, 3} {1, 2, 3} is always one-one. Suppose f is not one-one, So, atleast two elements will have the same image If 1 & 2 have same image 1, & 3 has image 3 Then, 2 has no pre-image, Hence, f is not onto. But, given that f is onto, So, f must be one-one
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13 You are here
Example 14
Example 15
Example 16
Example 17
Example 18
Example 19
Example 20
Example 21
Example 22
Example 23 Important
Example 24
Example 25 Important
Example 26
Example 27
Example 28
Example 29
Example 30
Example 31
Example 32
Example 33
Example 34
Example 35
Example 36
Example 37
Example 38
Example 39
Example 40
Example 41
Example 42
Example 43
Example 44
Example 45
Example 46 Important
Example 47 Important
Example 48 Important
Example 49
Example 50
Example 51
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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.