Check sibling questions

Ex 1.2, 11 - Let f(x) = x4. Choose (A) f is one-one onto

Ex 1.2 , 11 - Chapter 1 Class 12 Relation and Functions - Part 2
Ex 1.2 , 11 - Chapter 1 Class 12 Relation and Functions - Part 3
Ex 1.2 , 11 - Chapter 1 Class 12 Relation and Functions - Part 4

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


Transcript

Ex 1.2, 11 Let f: R → R be defined as f(x) = x4. 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) = x4 Checking one-one f (x1) = (x1)4 f (x2) = (x2)4 Putting f (x1) = f (x2) (x1)4 = (x2)4 x1 = x2 or x1 = –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 Since x1 does not have unique image, It is not one-one Eg: f(–1) = (–1)4 = 1 f(1) = (1)4 = 1 Here, f(–1) = f(1) , but –1 ≠ 1 Hence, it is not one-one Check onto f(x) = x4 Let f(x) = y , such that y ∈ R x4 = y x = ±𝑦^(1/4) Note that y is a real number, it can be negative also Putting y = −3 x = ±〖(−3)〗^(1/4) x = ± (√(−3))^(1/2) Which is not possible as root of negative number is not real Hence, x is not real ∴ f is not onto Hence, f is neither one-one nor onto Option D is correct

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.