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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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