# Example 9 - Chapter 1 Class 12 Relation and Functions (Term 1)

Last updated at Sept. 25, 2018 by Teachoo

Last updated at Sept. 25, 2018 by Teachoo

Transcript

Example 9 Prove that the function f : R → R, given by f (x) = 2x, is one-one and onto. f(x) = 2x Checking one-one f (x1) = 2x1 f (x2) = 2x2 Putting f(x1) = f(x2) 2x1 = 2 x2 x1 = x2. Hence, if f(x1) = f(x2) , x1 = x2 ∴ function f is one-one Onto f(x) = 2x Let f(x) = y, , such that y ∈ R 2x = y x = 𝑦2 Since y is a real number, Hence 𝑦2 will also be a real number So, x will also be a real number, i.e., x ∈ R Hence, f is onto

Examples

Example 1

Example 2

Example 3

Example 4 Important

Example 5

Example 6 Important

Example 7

Example 8 Important

Example 9 You are here

Example 10

Example 11 Important

Example 12 Important

Example 13 Important

Example 14 Important

Example 15 Deleted for CBSE Board 2022 Exams

Example 16 Deleted for CBSE Board 2022 Exams

Example 17 Deleted for CBSE Board 2022 Exams

Example 18 Important Deleted for CBSE Board 2022 Exams

Example 19 Important Deleted for CBSE Board 2022 Exams

Example 20 Deleted for CBSE Board 2022 Exams

Example 21 Deleted for CBSE Board 2022 Exams

Example 22 Deleted for CBSE Board 2022 Exams

Example 23 Important Deleted for CBSE Board 2022 Exams

Example 24 Deleted for CBSE Board 2022 Exams

Example 25 Important Deleted for CBSE Board 2022 Exams

Example 26 Deleted for CBSE Board 2022 Exams

Example 27 Important Deleted for CBSE Board 2022 Exams

Example 28 (a) Deleted for CBSE Board 2022 Exams

Example 28 (b) Deleted for CBSE Board 2022 Exams

Example 28 (c) Deleted for CBSE Board 2022 Exams

Example 29 Deleted for CBSE Board 2022 Exams

Example 30 Deleted for CBSE Board 2022 Exams

Example 31 Important Deleted for CBSE Board 2022 Exams

Example 32 Deleted for CBSE Board 2022 Exams

Example 33 Deleted for CBSE Board 2022 Exams

Example 34 Deleted for CBSE Board 2022 Exams

Example 35 Deleted for CBSE Board 2022 Exams

Example 36 Deleted for CBSE Board 2022 Exams

Example 37 Important Deleted for CBSE Board 2022 Exams

Example 38 Deleted for CBSE Board 2022 Exams

Example 39 Deleted for CBSE Board 2022 Exams

Example 40 Deleted for CBSE Board 2022 Exams

Example 41

Example 42 Important

Example 43 Important

Example 44

Example 45 (a) Deleted for CBSE Board 2022 Exams

Example 45 (b) Deleted for CBSE Board 2022 Exams

Example 46 Important Deleted for CBSE Board 2022 Exams

Example 47 Important Deleted for CBSE Board 2022 Exams

Example 48 Important Deleted for CBSE Board 2022 Exams

Example 49 Deleted for CBSE Board 2022 Exams

Example 50

Example 51 Important

Chapter 1 Class 12 Relation and Functions (Term 1)

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 10 years. He provides courses for Maths and Science at Teachoo.