Example 19 - Show that if f, g are onto, then gof is also onto - Composite funcions and one-one onto

  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise


Example 19 Show that if f : A B and g : B C are onto, then gof : A C is also onto. Since g : B C is onto Suppose z C, then there exists a pre-image in B Let the pre-image be y Hence, y B such that g (y) = z Similarly, since f : A B is onto If y B, then there exists a pre-image in A Let the pre-image be x Hence, x A such that f(x) = y Now, gof = g(f(x)) = g (y) = z So, for every x in A, there is an image z in C , thus, gof is onto.

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.