Question 5 - Miscellaneous - Chapter 1 Class 12 Relation and Functions

Last updated at April 16, 2024 by

Misc 7 - Give examples of f, g - gof is onto but f is not onto - Miscellaneous

Misc 7 - Chapter 1 Class 12 Relation and Functions - Part 2
Misc 7 - Chapter 1 Class 12 Relation and Functions - Part 3
Misc 7 - Chapter 1 Class 12 Relation and Functions - Part 4

Transcript

Question 5 Given examples of two functions f: N N and g: N N such that gof is onto but f is not onto. (Hint: Consider f(x) = x + 1 and g (x) = 1, >1 &1, =1 ) Let f: N N be f(x) = x + 1 And, g: N N be, g (x) = 1, >1 &1, =1 We will first show that f is not onto. Checking f is not onto f: N N be f(x) = x + 1 Let y = f(x), where y N So, y = x + 1 y 1 = x x = y 1 For y = 1, x = 1 1 = 0 But 0 is not a natural number f is not onto. Finding gof f(x) = x + 1 & g (x) = 1, >1 &1, =1 So, gof = , >1 1, =1 Let gof = y , where y N So, y = , >1 1, =1 Here y is a natural number , As y = x So, x is also a natural number Hence, gof is onto.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.