Check sibling questions

Ex 1.2, 3 - Prove that Greatest Integer Function f(x) = [x] - To prove injective/ surjective/ bijective (one-one & onto)

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

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Ex 1.2 , 3 (Introduction) Prove that the Greatest Integer Function f: R R given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x. f(x) = [x] = greatest integer less than equal to x Example: [1] = 1 [1.01] = 1 [1.2] = 1 [1.9] = 1 [1.99] = 1 [2] = 2 Ex 1.2 , 3 Prove that the Greatest Integer Function f: R R given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x. f(x) = [x] where [x] denotes the greatest integer less than equal to x Check one-one f(x) = [x] Eg: f(1) = [1] = 1, f(1.2) = [1.2] = 1, f(1.9) = [1.9] = 1, f(1.99) = [1.99] = 1, Check onto f(x) = [x] Let y = f(x) y = [x] i.e. y = Greatest integer less than or equal to x Hence, value of y will always come an integer. But y is a real number Hence f is not onto.

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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.