Check the Injectivity and Surjectivity of (ii) f: Z → Z,  f(x) = x^3 - Ex 1.2

part 2 - Ex 1.2, 2 (v) - Ex 1.2 - Serial order wise - Chapter 1 Class 12 Relation and Functions
part 3 - Ex 1.2, 2 (v) - Ex 1.2 - Serial order wise - 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: (v) f: Z → Z given by f(x) = x3 f(x) = x3 Checking one-one (injective) f (x1) = (x1)3 f (x2) = (x2)3 Now, f (x1) = f (x2) (x1)3 = (x2)3 x1 = x2 Since if f (x1) = f (x2) , then x1 = x2 ∴ It is one-one (injective) Check onto (surjective) f(x) = x3 Let f(x) = y , such that y ∈ Z x3 = y x = 𝒚^(𝟏/𝟑) Here y is an integer i.e. y ∈ Z Let y = 2 x = 𝑦^(1/3) = 𝟐^(𝟏/𝟑) So, x is not an integer ∴ f is not onto (not surjective) Hence, function f is injective but 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo