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Ex 1.2, 5 - Chapter 1 Class 12 Relation and Functions
Last updated at May 29, 2023 by Teachoo
Ex 1.2
Ex 1.2, 1
Ex 1.2, 2 (i) Important
Ex 1.2, 2 (ii) Important
Ex 1.2, 2 (iii)
Ex 1.2, 2 (iv)
Ex 1.2, 2 (v) Important
Ex 1.2 , 3
Ex 1.2 , 4
Ex 1.2, 5 Important You are here
Ex 1.2 , 6 Important
Ex 1.2, 7 (i)
Ex 1.2, 7 (ii)
Ex 1.2 , 8 Important
Ex 1.2 , 9
Ex 1.2 , 10 Important
Ex 1.2 , 11 (MCQ) Important
Ex 1.2, 12 (MCQ)
Transcript
Ex 1.2, 5 Show that the Signum Function f: R β R, given by f(x) = {β(1 for π₯ >0@ 0 for π₯=0@β1 for π₯<0)β€ is neither one-one nor onto. f(x) = {β(1 for π₯ >0@ 0 for π₯=0@β1 for π₯<0)β€ For example: f(0) = 0 f(-1) = β1 f(1) = 1 f(2) = 1 f(3) = 1 Since, different elements 1,2,3 have the same image 1 , β΄ f is not one-one. Check onto f: R β R f(x) = {β(1 for π₯ >0@ 0 for π₯=0@β1 for π₯<0)β€ Value of f(x) is defined only if x is 1, 0, β1 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
