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. 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.

Class 12, NCERT Chapter 1,  Exercise 1.2, Q12

f: R → R defined as f(x) = 3x.

Let x, y ∈ R such that f(x) = f(y).
⇒ 3x = 3y
⇒ x = y
∴f is one-one.
Also, for any real number (y) in co-domain R, there exists in R such that.
∴f is onto.
Hence, function f is one-one and onto.
The correct answer is A.
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  1. Hemant KK Singh16 August 2020 at 16:13

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