Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma maths class 12 chapter Functions exercise 2.1 question 5 sub question (iv)

Need solution for RD Sharma maths class 12 chapter Functions exercise 2.1 question 5 sub question (iv)

Answers (1)

Injective but not surjective.

Given:

f:Z \rightarrow Z given byf(x)=x^3  

Hint:

One-one function means every element in the domain has a distinct image in the  co-domain.

Onto function means every element in the co-domain has at least one  pre image in the domain of function.

For any function to be a bijective, the given function be one-one and onto.

Solution:

Let us check for the given function is injection, surjection and bijection.

Let's start with the injection test.

Let x and y be any two elements in the domain (N) such thatf(x)=f(y)

    \begin{aligned} &f(x)=x^{3}, f(y)=y^{3} \\ &f(x)=f(y) \\ &x^{3}=y^{3} \\ &x=y \end{aligned}

So,f is an injection

Surjection test:

Let y be any element in the codomain (N) , such thatf(x)=y  for some element x in N .

 f(x)=y

x^3=y

x=\sqrt[3]{y} which may not be in N

So,f is not a surjection.

Here f is injective but not surjective, so the f is not a bijection.

The condition of bijection is as we know the function should be one-one and onto.

Hence for this, f is not bijection.

Posted by

infoexpert24

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

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question