# Example 50 - Chapter 1 Class 12 Relation and Functions (Term 1)

Last updated at Jan. 30, 2020 by Teachoo

Last updated at Jan. 30, 2020 by Teachoo

Transcript

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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Example 50 You are here

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Chapter 1 Class 12 Relation and Functions (Term 1)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.