Solve all your doubts with Teachoo Black (new monthly pack available now!)

Are you in **school**? Do you **love Teachoo?**

We would love to talk to you! Please fill this form so that we can contact you

Ex 1.2

Ex 1.2, 1

Ex 1.2, 2 (i) Important

Ex 1.2, 2 (ii) Important

Ex 1.2, 2 (iii)

Ex 1.2, 2 (iv)

Ex 1.2, 2 (v) Important

Ex 1.2 , 3

Ex 1.2 , 4

Ex 1.2, 5 Important

Ex 1.2 , 6 Important

Ex 1.2, 7 (i)

Ex 1.2, 7 (ii)

Ex 1.2 , 8 Important

Ex 1.2 , 9

Ex 1.2 , 10 Important

Ex 1.2 , 11 (MCQ) Important

Ex 1.2, 12 (MCQ) You are here

Chapter 1 Class 12 Relation and Functions

Serial order wise

Last updated at Aug. 6, 2021 by Teachoo

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