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Example 50 - Consider the identity function IN (x) = x - Examples

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  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
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Example 50 Consider the identity function IN : N → N defined as IN (x) = x ∀ x ∈ N. Show that although IN is onto but IN + IN : N → N defined as (IN + IN) (x) = IN (x) + IN (x) = x + x = 2x is not onto. IN : N → N IN (x) = x Let y = IN (x) , such that y ∈ N So, y = x Since, x is natural number y is a natural number So, IN is onto. Now, IN + IN (x) = x + x = 2x ∴ IN + IN (x) = 2x Let y = IN + IN (x) , such that y ∈ N So y = 2x 2x = y x = 𝑦﷮2﷯ If y = 1, x = 1﷮2﷯ = 0.5 , which is not a natural number Hence, IN+ IN is not onto

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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