40 votes 40 votes Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE? $f$ and $g$ should both be onto functions $f$ should be onto but $g$ need not to be onto $g$ should be onto but $f$ need not be onto both $f$ and $g$ need not be onto Set Theory & Algebra gatecse-2005 set-theory&algebra functions normal + – gatecse asked Sep 21, 2014 edited Nov 28, 2015 by Akash Kanase gatecse 9.9k views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments HitechGa commented Jul 12, 2021 reply Follow Share I found many people answered using diagrams but did not mark the blue links as shown. These blue links are necessary as f is a function, 8 votes 8 votes Venky8 commented Sep 18, 2021 i edited by Venky8 Sep 18, 2021 reply Follow Share One more possible diagram, just for better understanding. 1 votes 1 votes Mohitdas commented Dec 10, 2021 reply Follow Share …………………………………………………………………………… 1 votes 1 votes Please log in or register to add a comment.
1 votes 1 votes Option b will be correct as f is required to be onto while g need not necessary be onto as depicted by below example. harypotter0 answered Jul 11, 2020 harypotter0 comment Share Follow See all 2 Comments See all 2 2 Comments reply PratikDey0316 commented Nov 25, 2020 reply Follow Share $A = {1,2,3} B = {1,2,3,4} C = {10,11,12,20} g:A->B => {(1,1),(2,2), (3,3)} f:B->C => {(1,10),(2,11),(3,12),(4,20)} Lets consider this example in this example f is onto but g is not onto. But if you see then fog(x) is not coming out to be onto 0 votes 0 votes rajankakaniya commented Jun 15, 2021 reply Follow Share But here it is given that h=fog is onto. We should take example in that h is onto then check. @PratikDey0316 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Option (B) is correct. Mostafize Mondal answered Sep 15, 2018 edited Dec 1, 2018 by Mostafize Mondal Mostafize Mondal comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes so option b is correct option f should be onto but g need not to be onto akshay_123 answered Sep 26, 2023 akshay_123 comment Share Follow See all 0 reply Please log in or register to add a comment.