Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Show that the function f : R → R given by f (x) = x ^3 is injective.

Q.5 Show that the function f : R \rightarrow R given by f (x) = x ^3 is injective.

Answers (1)

best_answer

f : R \rightarrow R

f (x) = x ^3

One-one:

   Let    f(x)=f(y)\, \, \, \, \, \, x,y \in R

             x^{3}=y^{3}

We need to prove x=y.So,

  • Let    x\neq y then there cubes will not be equal i.e. x^{3}\neq y^{3}.
  •  It will contradict given condition of cubes being equal. 
  • Hence, x=y  and it is one -one which means it is injective.
  •  

 

 

 

 

 

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Board Exams 2025: Guidelines issued for Class 10, 12 practicals
anam-khan

Board Exam Date Sheet 2025 Live: ICSE, ISC, CBSE, MP time table out; BSEB routine soon
anam-khan

Board exam dates 2025: CBSE, CISCE, UP, MP, Maharashtra, TN time table out; state-wise updates

Latest Question