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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
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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.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.