The function ๐‘“: RโŸถ R defined as ๐‘“(๐‘ฅ) = ๐‘ฅ3 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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  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 21 The function ๐‘“: RโŸถ R defined as ๐‘“(๐‘ฅ) = ๐‘ฅ3 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 โˆด x1 = x2 Since if f(x1) = f(x2) , then x1 = x2 โˆด It is one-one Check onto f(x) = x3 Let f(x) = y , such that y โˆˆ R x3 = y x = ๐’š^(๐Ÿ/๐Ÿ‘) Here y is a real number i.e. y โˆˆ R And, For all values of y, we will get a value of x, Where x โˆˆ 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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.