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  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise

Transcript

Ex 1.2, 5 Show that the Signum Function f: R โ†’ R, given by f(x) = {โ–ˆ(1 for ๐‘ฅ >0@ 0 for ๐‘ฅ=0@โˆ’1 for ๐‘ฅ<0)โ”ค is neither one-one nor onto. f(x) = {โ–ˆ(1 for ๐‘ฅ >0@ 0 for ๐‘ฅ=0@โˆ’1 for ๐‘ฅ<0)โ”ค For example: f(0) = 0 f(-1) = โˆ’1 f(1) = 1 f(2) = 1 f(3) = 1 Since, different elements 1,2,3 have the same image 1 , โˆด f is not one-one. Check onto f: R โ†’ R f(x) = {โ–ˆ(1 for ๐‘ฅ >0@ 0 for ๐‘ฅ=0@โˆ’1 for ๐‘ฅ<0)โ”ค Value of f(x) is defined only if x is 1, 0, โ€“1 For other real numbers(eg: y = 2, y = 100) there is no corresponding element x Hence f is not onto Thus, f is neither one-one nor onto

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.