Example 10 - 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 You are here
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
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 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