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Last updated at Jan. 28, 2020 by Teachoo

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Ex 1.2, 12 Let f: R → R be defined as f(x) = 3x. Choose the correct answer. (A) f is one-one ,onto (B) f is many-one onto (C) f is one-one but not onto (D) f is neither one-one nor onto f(x) = 3x Checking one-one f (x1) = 3x1 f (x2) = 3x2 Putting f(x1) = f(x2) 3x1 = 3 x2 Rough One-one Steps: 1. Calculate f(x1) 2. Calculate f(x2) 3. Putting f(x1) = f(x2) we have to prove x1 = x2 x1 = x2 Hence, if f(x1) = f(x2) , x1 = x2 ∴ function f is one-one Onto f(x) = 3x Let f(x) = y , such that y ∈ R 3x = y x = 𝑦/3 Now, Checking for y = f(x) Putting value of x in f(x) f(x) = f(𝑦/3) = 3(y/3) = 𝑦 Thus, for every y ∈ R, there exists x ∈ R such that f(x) = y Hence, f is onto So, f is one-one and onto ∴ A is the correct option

To prove one-one & onto (injective, surjective, bijective)

One One function

Onto function

One One and Onto functions (Bijective functions)

Example 7

Example 8

Example 9

Example 11 Important

Misc 5

Ex 1.2, 5 Important

Ex 1.2 , 6

Example 10

Ex 1.2, 1

Ex 1.2, 12 You are here

Ex 1.2 , 2 Important

Ex 1.2 , 7

Ex 1.2 , 11

Example 12 Important

Ex 1.2 , 9

Ex 1.2 , 3

Ex 1.2 , 4

Example 50

Example 51 Important

Ex 1.2 , 10 Important

Misc. 4 Important

Example 13 Important

Example 14 Important

Ex 1.2 , 8 Important

Example 46 Important

Misc 10 Important

Chapter 1 Class 12 Relation and Functions

Concept wise

- Relations - Definition
- Empty and Universal Relation
- To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
- Function - Definition
- To prove one-one & onto (injective, surjective, bijective)
- Composite functions
- Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse

About the Author

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.