Example 8 - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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
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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