![Slide18.JPG](https://d1avenlh0i1xmr.cloudfront.net/3f7b1bbd-b6c4-4d2b-ab73-f03e29b5cc3b/slide18.jpg)
Examples
Last updated at April 16, 2024 by Teachoo
Example 8 Show that the function f : Nā 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 ā N 2x = y x = š¦/2 If y = 1 x = 1/2 = 0.5 , which is not possible as x ā N Hence, f is not onto