Example 28 - Let S = {1, 2, 3}. Determine if inverse. Find f-1 - Examples

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  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
  3. Examples

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    Example 15 Not in Syllabus - CBSE Exams 2021

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    Example 27 Important Not in Syllabus - CBSE Exams 2021

    Example 28 Not in Syllabus - CBSE Exams 2021 You are here

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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)}

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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

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Example 45 Important Not in Syllabus - CBSE Exams 2021

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Example 51 Important

About the Author

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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.