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# Let F: R → R Be Defined As F(X) = 3x. Choose the Correct Answer. F Is One-one onto (B) F Is Many-one onto F Is One-one but Not onto (D) F Is Neither One-one Nor onto - CBSE (Commerce) Class 12 - Mathematics

#### Question

Let fR → 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

#### Solution

fR → R is defined as f(x) = 3x.

Let x∈ R such that f(x) = f(y).

⇒ 3x = 3y

⇒ x = y

is one-one.

Also, for any real number (y) in co-domain R, there exists y/3 in R such that f(y/3) = 3(y/3) = y.

is onto.

Hence, function f is one-one and onto.