Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Examples

Example 1

Example 2

Example 3

Example 4 Important

Example 5

Example 6 Important

Example 7

Example 8 Important

Example 9

Example 10

Example 11 Important

Example 12 Important You are here

Example 13 Important

Example 14 Important

Example 15

Example 16

Example 17 Important

Example 18

Example 19 Important

Example 20 Important

Example 21

Example 22 Important

Example 23 Important

Example 24 Important

Example 25

Example 26 Important

Question 1 Deleted for CBSE Board 2024 Exams

Question 2 Important Deleted for CBSE Board 2024 Exams

Question 3 Important Deleted for CBSE Board 2024 Exams

Question 4 Deleted for CBSE Board 2024 Exams

Question 5 Deleted for CBSE Board 2024 Exams

Question 6 Deleted for CBSE Board 2024 Exams

Question 7 Deleted for CBSE Board 2024 Exams

Question 8 Important Deleted for CBSE Board 2024 Exams

Question 9 Deleted for CBSE Board 2024 Exams

Question 10 Important Deleted for CBSE Board 2024 Exams

Question 11 (a) Deleted for CBSE Board 2024 Exams

Question 11 (b) Deleted for CBSE Board 2024 Exams

Question 11 (c) Deleted for CBSE Board 2024 Exams

Question 12 Deleted for CBSE Board 2024 Exams

Question 13 Deleted for CBSE Board 2024 Exams

Question 14 Important Deleted for CBSE Board 2024 Exams

Question 15 Deleted for CBSE Board 2024 Exams

Question 16 Deleted for CBSE Board 2024 Exams

Question 17 Deleted for CBSE Board 2024 Exams

Question 18 Deleted for CBSE Board 2024 Exams

Question 19 Deleted for CBSE Board 2024 Exams

Question 20 Important Deleted for CBSE Board 2024 Exams

Question 21 Deleted for CBSE Board 2024 Exams

Question 22 Deleted for CBSE Board 2024 Exams

Question 23 Deleted for CBSE Board 2024 Exams

Question 24 (a) Deleted for CBSE Board 2024 Exams

Question 24 (b) Deleted for CBSE Board 2024 Exams

Question 25 Deleted for CBSE Board 2024 Exams

Chapter 1 Class 12 Relation and Functions

Serial order wise

Last updated at June 6, 2023 by Teachoo

Example 12 Show that f : N → N, given by f(x) = {█(𝑥+1 , 𝑖𝑓 𝑥 𝑖𝑠 𝑜𝑑𝑑@𝑥−1, 𝑖𝑓 𝑥 𝑖𝑠 𝑒𝑣𝑒𝑛)┤ is both one-one and onto. Check one-one There can be 3 cases x1 & x2 both are odd x1 & x2 both are even x1 is odd & x2 is even If x1 & x2 are both odd f(x1) = x1 + 1 f(x2) = x2 + 1 Putting f(x1) = f(x2) x1 + 1 = x2 + 1 x1 = x2 If x1 & x2 are both are even f(x1) = x1 – 1 f(x2) = x2 – 1 If f(x1) = f(x2) x1 – 1 = x2 – 1 x1 = x2 If x1 is odd and x2 is even f(x1) = x1 + 1 f(x2) = x2 – 1 If f(x1) = f(x2) x1 + 1 = x2 – 1 x2 – x1 = 2 which is impossible as difference between even and odd number can never be even Hence, if f(x1) = f(x2) , Then x1 = x2 ∴ function f is one-one If x is odd f(x) = x + 1 y = x + 1 y – 1 = x x = y – 1 If x is odd, y is even Check onto f(x) = {█(𝑥+1 , 𝑖𝑓 𝑥 𝑖𝑠 𝑜𝑑𝑑@𝑥−1, 𝑖𝑓 𝑥 𝑖𝑠 𝑒𝑣𝑒𝑛)┤ Let f(x) = y , such that y ∈ N x = {█(𝑦−1 , 𝑖𝑓 𝑦 𝑖𝑠 𝑒𝑣𝑒𝑛@𝑦+1, 𝑖𝑓 𝑦 𝑖𝑠 𝑜𝑑𝑑)┤ If x is even f(x) = x – 1 y = x – 1 y + 1 = x x = y + 1 If x is even, y is odd Hence, if y is a natural number, x will also be a natural number i.e. x ∈ N Thus, f is onto.