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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 ) = 3 x . Let  x ,  y  ∈  R  such that  f ( x ) =  f ( y ). ⇒ 3 x  = 3 y ⇒  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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Class 12, NCERT Chapter 1,  Exercise 1.2, Q9 Thus it is bijective.
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Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

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