Example 9 - Chapter 1 Class 12 Relation and Functions

Last updated at Dec. 16, 2024 by

Example 9 - Prove that f(x) = 2x is one-one and onto - Chapter 1 - Examples

part 2 - Example 9 - Examples - Serial order wise - Chapter 1 Class 12 Relation and Functions

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Example 9 Prove that the function f : R → R, given by f (x) = 2x, is one-one and onto. f(x) = 2x Checking 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 ∈ R 2x = y x = 𝑦/2 Since y is a real number, Hence 𝑦/2 will also be a real number So, x will also be a real number, i.e., x ∈ R 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