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Ex 1.2, 2 (i) - Chapter 1 Class 12 Relation and Functions (Term 1)
Last updated at March 30, 2023 by Teachoo
Ex 1.2
Ex 1.2, 1
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, 5 Important
Ex 1.2 , 6 Important
Ex 1.2, 7 (i)
Ex 1.2, 7 (ii)
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Ex 1.2 , 10 Important
Ex 1.2 , 11 (MCQ) Important
Ex 1.2, 12 (MCQ)
Chapter 1 Class 12 Relation and Functions
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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)
