Example 25 - Chapter 1 Class 12 Relation and Functions

Last updated at Dec. 16, 2024 by

Example 25 - Consider Identity function In = X. Show that In is onto - Examples

part 2 - Example 25 - Examples - Serial order wise - Chapter 1 Class 12 Relation and Functions

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Example 25 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo