Ex 1.2, 2 (i) - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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 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)
Ex 1.2
Ex 1.2, 2 (i) Important You are here
Ex 1.2, 2 (ii) Important
Ex 1.2, 2 (iii)
Ex 1.2, 2 (iv)
Ex 1.2, 2 (v) Important
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Ex 1.2, 7 (i)
Ex 1.2, 7 (ii)
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Ex 1.2 , 11 (MCQ) Important
Ex 1.2, 12 (MCQ)
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo