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Let f : R → R be defined as f(x) = 3x. Choose the correct answer. - Mathematics

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Question

Let f : R → R be defined as f(x) = 3x. Choose the correct answer.

Options

  • f is one-one onto.

  • f is many-one onto.

  • f is one-one but not onto.

  • f is neither one-one nor onto.

MCQ
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Solution

f is one-one onto.

Explanation:

Let x1, x2 ∈ R such that f(x1) = f(x2)

⇒ 3x1 = 3x2

⇒ x1 = x2

∴ f is one-one.

Consider any y ∈ R (co-domain of f); there exist x ∈ R (domain of f) such that:

f(x) = y

⇒ 3x = y

⇒ x = `y/3`

∴ `f(y/3) = 3.y/3` = y

∴ f is onto.

Hence, f is one-one onto.

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Chapter 1: Relations and Functions - Exercise 1.2 [Page 11]

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NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 1 Relations and Functions
Exercise 1.2 | Q 12 | Page 11

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