Example 10 - Chapter 1 Class 12 Relation and Functions

Last updated at August 13, 2026 by

Example 10 - Show f(1) = f(2) = 1 and f (x) = x - 1 is onto - Examples

part 2 - Example 10 - Examples - Serial order wise - Chapter 1 Class 12 Relation and Functions

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Transcript

Example 10 Show that the function f : N ā†’ N, given by f (1) = f (2) = 1 and f (x) = x ā€“ 1, for every x > 2, is onto but not one-one. Here, f(x) = {ā–ˆ( 1 for š‘„=1@ 1 for š‘„=2@š‘„āˆ’1 for š‘„>2)ā”¤ Here, f (1) = 1 f (2) = 1 Check onto f: N ā†’ N f(x) = {ā–ˆ( 1 for š‘„=1@ 1 for š‘„=2@š‘„āˆ’1 for š‘„>2)ā”¤ Let f(x) = y , such that y āˆˆ N Here, y is a natural number & for every y, there is a value of x which is a natural number Hence f is onto

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