Question 3 - Examples - Chapter 1 Class 12 Relation and Functions

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Example 19 - Show that if f, g are onto, then gof is also onto

Example 19 - Chapter 1 Class 12 Relation and Functions - Part 2

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Question 3 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 : A → C 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 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 and Computer Science at Teachoo