Example 10 - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 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
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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