Check sibling questions

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

Last updated at May 29, 2023 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

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Book a free demo

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.

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.