Class 12 Mathematics - Chapter Relations and Functions NCERT Solutions | Let f : R → R be defined as f(x) =
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: 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.
More Questions From Class 12 Mathematics - Chapter Relations and Functions
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(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
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(b) R = {(x, y): x and y live in the same locality}
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- Q:- Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric.
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