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 March 22, 2023 by Teachoo
The function π: RβΆ R defined as π(π₯) = π₯3 is:
(a) One-on but not ontoΒ (b) Not one-one but onto
(c) Neither one-one nor ontoΒ (d) One-one and onto
This question is
inspired from
Question 1 (Choice 1)
-
CBSE Class 12 Sample Paper for 2021 Boards
This video is only available for Teachoo black users
Question 21 The function π: RβΆ R defined as π(π₯) = π₯3 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
β΄ x1 = x2
Since if f(x1) = f(x2) , then x1 = x2
β΄ It is one-one
Check onto
f(x) = x3
Let f(x) = y , such that y β R
x3 = y
x = π^(π/π)
Here y is a real number i.e. y β R
And, For all values of y, we will get a value of x,
Where x β R
So, f is onto
Thus, f is one-one and onto
So, the correct answer is (d)
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
Hi, it looks like you're using AdBlock :(
Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.
Please login to view more pages. It's free :)
Teachoo gives you a better experience when you're logged in. Please login :)
Solve all your doubts with Teachoo Black!
Teachoo answers all your questions if you are a Black user!