Ex 1.2, 12 - Let f(x) = 3x. Choose (A) f is one-one onto - To prove injective/ surjective/ bijective (one-one & onto)

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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 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﷯ Since y is a real number, Hence 𝑦﷮3﷯ will also be a real number So, x will also be a real number, i.e., x ∈ R Hence, f is onto So, f is one-one and onto So, A is the correct option

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