Example 11 - Chapter 1 Class 12 Relation and Functions
Last updated at Nov. 5, 2018 by Teachoo
Transcript
Example 11 Show that the function f: R R, defined as f(x) = x2, is neither one-one nor onto f(x) = x2 Checking one-one f (x1) = (x1)2 f (x2) = (x2)2 f (x1) = f (x2) (x1)2 = (x2)2 x1 = x2 or x1 = x2 Since x1 does not have unique image, It is not one-one Eg: f( 1) = ( 1)2 = 1 f(1) = (1)2 = 1 Here, f( 1) = f(1) , but 1 1 Hence, it is not one-one Check onto f(x) = x2 Let f(x) = y , such that y R x2 = y x = Note that y is a real number, so it can be negative also Putting y = 3 x = ( 3) Hence, x is not real So, f is not onto
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Chapter 1 Class 12 Relation and Functions
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.