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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  1. Chapter 1 Class 12 Relation and Functions
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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 𝑥=1﷮ 1 for 𝑥=2﷮𝑥−1 for 𝑥>2﷯﷯ Here, f (1) = 1 f (2) = 1. Check onto f: N → N f(x) = 1 for 𝑥=1﷮ 1 for 𝑥=2﷮𝑥−1 for 𝑥>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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