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Ex 1.2, 12 Let f: R → R be defined as f(x) = 3x. Choose the correct answer. (A) f is one-one ,onto (B) f is many-one onto (C) f is one-one but not onto (D) f is neither one-one nor onto f(x) = 3x Checking one-one f (x1) = 3x1 f (x2) = 3x2 Putting f(x1) = f(x2) 3x1 = 3 x2 Rough One-one Steps: 1. Calculate f(x1) 2. Calculate f(x2) 3. Putting f(x1) = f(x2) we have to prove x1 = x2 x1 = x2 Hence, if f(x1) = f(x2) , x1 = x2 ∴ function f is one-one Onto f(x) = 3x Let f(x) = y , such that y ∈ R 3x = y x = 𝑦/3 Now, Checking for y = f(x) Putting value of x in f(x) f(x) = f(𝑦/3) = 3(y/3) = 𝑦 Thus, for every y ∈ R, there exists x ∈ R such that f(x) = y Hence, f is onto So, f is one-one and onto ∴ A is the correct option

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.