Ex 1.2, 2 - Check injectivity and surjectivity of (i) f(x) = x^2,

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

  1. Chapter 1 Class 12 Relation and Functions (Term 1)
  2. Serial order wise

Transcript

Ex 1.2, 2 Check the injectivity and surjectivity of the following functions: (i) f: N → N given by f(x) = x2 f(x) = x2 Checking one-one (injective) f (x1) = (x1)2 f (x2) = (x2)2 Putting f (x1) = f (x2) ⇒ (x1)2 = (x2)2 ⇒ 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 & x2 are natural numbers, they are always positive. Hence, x1 = x2 Hence, it is one-one (injective) Check onto (surjective) f(x) = x2 Let f(x) = y , such that y ∈ N x2 = y x = ±√𝑦 Putting y = 2 x = √2 = 1.41 Since x is not a natural number Given function f is not onto So, f is not onto (not surjective)

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
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.