Check sibling questions

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

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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)

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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.