Example 25 - Chapter 1 Class 12 Relation and Functions
Last updated at April 16, 2024 by Teachoo
To prove one-one & onto (injective, surjective, bijective)
Onto function
One One and Onto functions (Bijective functions)
Example 7
Example 8 Important
Example 9
Example 11 Important
Misc 2
Ex 1.2, 5 Important
Ex 1.2 , 6 Important
Example 10
Ex 1.2, 1
Ex 1.2, 12 (MCQ)
Ex 1.2, 2 (i) Important
Ex 1.2, 7 (i)
Ex 1.2 , 11 (MCQ) Important
Example 12 Important
Ex 1.2 , 9
Ex 1.2 , 3
Ex 1.2 , 4
Example 25 You are here
Example 26 Important
Ex 1.2 , 10 Important
Misc 1 Important
Example 13 Important
Example 14 Important
Ex 1.2 , 8 Important
Example 22 Important
Misc 4 Important
To prove one-one & onto (injective, surjective, bijective)
Last updated at April 16, 2024 by Teachoo
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