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Ex 1.2, 5 - Show Signum Function is neither one-one nor onto

Ex 1.2, 5 - Chapter 1 Class 12 Relation and Functions - Part 2


Transcript

Ex 1.2, 5 Show that the Signum Function f: R β†’ R, given by f(x) = {β–ˆ(1 for π‘₯ >0@ 0 for π‘₯=0@βˆ’1 for π‘₯<0)─ is neither one-one nor onto. f(x) = {β–ˆ(1 for π‘₯ >0@ 0 for π‘₯=0@βˆ’1 for π‘₯<0)─ For example: f(0) = 0 f(-1) = βˆ’1 f(1) = 1 f(2) = 1 f(3) = 1 Since, different elements 1,2,3 have the same image 1 , ∴ f is not one-one. Check onto f: R β†’ R f(x) = {β–ˆ(1 for π‘₯ >0@ 0 for π‘₯=0@βˆ’1 for π‘₯<0)─ Value of f(x) is defined only if x is 1, 0, –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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.