



Subscribe to our Youtube Channel - https://you.tube/teachoo
Last updated at Dec. 23, 2019 by Teachoo
Transcript
Example 28 Let S = {1, 2, 3}. Determine whether the functions f : S → S defined as below have inverses. Find f–1, if it exists. (a) f= {(1, 1), (2, 2), (3, 3)} A function has inverse if it is one-one and onto Check one one f = {(1, 1), (2, 2), (3, 3)} Since each element has unique image, f is one-one Check onto Since for every image, there is a corresponding element, ∴ f is onto. Since function is both one-one and onto it will have inverse f = {(1, 1), (2, 2), (3, 3)} f-1 = {(1, 1), (2, 2), (3, 3)} Example 28 Let S = {1, 2, 3}. Determine whether the functions f : S → S defined as below have inverses. Find f–1, if it exists. (b) f= {(1, 2), (2, 1), (3, 1)} A function has inverse if it is one-one and onto Check one one f = {(1, 2), (2, 1), (3, 1)} Since 2 & 3 have the same image 1 f is not one-one Since, f is not one-one, it does not have an inverse Example 28 Let S = {1, 2, 3}. Determine whether the functions f : S → S defined as below have inverses. Find f–1, if it exists. (c) f= {(1, 3), (3, 2), (2, 1)} A function has inverse if it is one-one and onto Check one one f = {(1, 3), (3, 2), (2, 1)} Since each element has unique image, f is one-one Check onto Since for every image, there is a corresponding element, ∴ f is onto. Since function is both one-one and onto it will have inverse f = {(1, 3), (3, 2), (2, 1)} f-1 = {(3, 1), (2, 3), (1, 2)}
Examples
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 Not in Syllabus - CBSE Exams 2021
Example 16 Not in Syllabus - CBSE Exams 2021
Example 17 Not in Syllabus - CBSE Exams 2021
Example 18 Important Not in Syllabus - CBSE Exams 2021
Example 19 Important Not in Syllabus - CBSE Exams 2021
Example 20 Not in Syllabus - CBSE Exams 2021
Example 21 Not in Syllabus - CBSE Exams 2021
Example 22 Not in Syllabus - CBSE Exams 2021
Example 23 Important Not in Syllabus - CBSE Exams 2021
Example 24 Not in Syllabus - CBSE Exams 2021
Example 25 Important Not in Syllabus - CBSE Exams 2021
Example 26 Not in Syllabus - CBSE Exams 2021
Example 27 Important Not in Syllabus - CBSE Exams 2021
Example 28 Not in Syllabus - CBSE Exams 2021 You are here
Example 29 Not in Syllabus - CBSE Exams 2021
Example 30 Not in Syllabus - CBSE Exams 2021
Example 31 Not in Syllabus - CBSE Exams 2021
Example 32 Not in Syllabus - CBSE Exams 2021
Example 33 Not in Syllabus - CBSE Exams 2021
Example 34 Not in Syllabus - CBSE Exams 2021
Example 35 Not in Syllabus - CBSE Exams 2021
Example 36 Not in Syllabus - CBSE Exams 2021
Example 37 Not in Syllabus - CBSE Exams 2021
Example 38 Not in Syllabus - CBSE Exams 2021
Example 39 Not in Syllabus - CBSE Exams 2021
Example 40 Not in Syllabus - CBSE Exams 2021
Example 41 Important
Example 42 Important
Example 43 Important
Example 44
Example 45 Important Not in Syllabus - CBSE Exams 2021
Example 46 Important
Example 47 Important
Example 48 Important
Example 49
Example 50
Example 51 Important
About the Author