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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

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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.

The correct answer is A.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 1: Relations and Functions
Q: 12 | Page no. 11
Solution 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 Concept: Types of Functions.
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