CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based  for Term 1)
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 Sept. 4, 2021 by Teachoo
The function ๐: Rโถ R defined as ๐(๐ฅ) = ๐ฅ3 is:
(a) Oneon but not onto (b) Not oneone but onto
(c) Neither oneone nor onto (d) Oneone and onto
This question is
inspired from
Question 1 (Choice 1)

CBSE Class 12 Sample Paper for 2021 Boards
Question 21 The function ๐: Rโถ R defined as ๐(๐ฅ) = ๐ฅ3 is: (a) Oneon but not onto (b) Not oneone but onto (c) Neither oneone nor onto (d) Oneone and onto
f(x) = x3
Checking oneone
f(x1) = (x1)3
f(x2) = (x2)3
Thus,
f (x1) = f (x2)
(x1)3 = (x2)3
โด x1 = x2
Since if f(x1) = f(x2) , then x1 = x2
โด It is oneone
Check onto
f(x) = x3
Let f(x) = y , such that y โ R
x3 = y
x = ๐^(๐/๐)
Here y is a real number i.e. y โ R
And, For all values of y, we will get a value of x,
Where x โ R
So, f is onto
Thus, f is oneone and onto
So, the correct answer is (d)
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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based  for Term 1)
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.