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

Transcript

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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