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Chapter 1 Class 12 Relation and Functions
Ex 1.2 , 10 Important
Example 23 Important Deleted for CBSE Board 2023 Exams
Example 25 Important Deleted for CBSE Board 2023 Exams
Ex 1.3, 3 (i) Important Deleted for CBSE Board 2023 Exams
Ex 1.3 , 6 Deleted for CBSE Board 2023 Exams
Ex 1.3 , 8 Important Deleted for CBSE Board 2023 Exams
Ex 1.3 , 9 Important Deleted for CBSE Board 2023 Exams
Ex 1.3, 13 (MCQ) Important Deleted for CBSE Board 2023 Exams
Ex 1.3, 14 (MCQ) Important Deleted for CBSE Board 2023 Exams
Ex 1.4, 11 Important Deleted for CBSE Board 2023 Exams
Misc 3 Important Deleted for CBSE Board 2023 Exams
Misc. 4 Important
Misc 14 Important Deleted for CBSE Board 2023 Exams
Misc 18
Chapter 1 Class 12 Relation and Functions
Last updated at Jan. 28, 2020 by Teachoo
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