Question 21 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by Teachoo

The function 𝑓: R⟶ R defined as 𝑓(𝑥) = 𝑥3 is:

(a) One-on but not onto (b) Not one-one but onto
(c) Neither one-one nor onto (d) One-one and onto

This question is inspired from Question 1 (Choice 1) - CBSE Class 12 Sample Paper for 2021 Boards

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Question 21 The function 𝑓: R⟶ R defined as 𝑓(𝑥) = 𝑥3 is: (a) One-on but not onto (b) Not one-one but onto (c) Neither one-one nor onto (d) One-one and onto f(x) = x3 Checking one-one f(x1) = (x1)3 f(x2) = (x2)3 Thus, f (x1) = f (x2) (x1)3 = (x2)3 ∴ x1 = x2 Since if f(x1) = f(x2) , then x1 = x2 ∴ It is one-one Check onto f(x) = x3 Let f(x) = y , such that y ∈ R x3 = y x = 𝒚^(𝟏/𝟑) Here y is a real number i.e. y ∈ R And, For all values of y, we will get a value of x, Where x ∈ R So, f is onto Thus, f is one-one and onto So, the correct answer is (d)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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