Example 10 - Show f(1) = f(2) = 1 and f (x) = x - 1 is onto - To prove injective/ surjective/ bijective (one-one & onto)

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Example 10 Show that the function f : N N, given by f (1) = f (2) = 1 and f (x) = x 1, for every x > 2, is onto but not one-one. Here, f(x) = 1 for =1 1 for =2 1 for >2 Here, f (1) = 1 f (2) = 1. Check onto f: N N f(x) = 1 for =1 1 for =2 1 for >2 Let f(x) = y , such that y 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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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.