web analytics

Example 8 - Show f(x) = 2x is one-one but not onto - To prove injective/ surjective/ bijective (one-one & onto)

Slide17.JPG

  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
Ask Download

Transcript

Example 8 Show that the function f : N→ N, given by f (x) = 2x, is one-one but not onto. Given, f(x) = 2x One-One f (x1) = 2x1 f (x2) = 2x2 Putting f(x1) = f(x2) 2x1 = 2 x2 x1 = x2. Hence, if f(x1) = f(x2) , x1 = x2 function f is one-one Onto f(x) = 2x Let f(x) = y , such that y ∈ N 2x = y x = 𝑦﷮2﷯ If y = 1 x = 1﷮2﷯ = 0.5 , which is not possible as x ∈ N Hence, f is not onto

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.
Jail