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 8 sub question (iii)

Need solution for RD Sharma maths class 12 chapter Functions exercise 2.1 question 8 sub question (iii)

Answers (1)

f is not bijective.

Given:

            h:A\rightarrow A, given byh(x)=(x)^2

To prove:

Function h is one-one, onto or bijective.

Hint:

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

Solution:

First we will check whether the given function is one-one or not.

We know for function h to be one-one

\begin{aligned} &\begin{aligned} & h\left(x_{1}\right)=h\left(x_{2}\right) \\ \Rightarrow & x_{1}^{2}=x_{2}^{2} \\ \Rightarrow & x_{1}=\pm x_{2} \end{aligned}\\ &\text { So, } h \text { is not one-one. } \end{aligned}

h(x)=x^2

Let h(x)=y such thaty \in A

y=x^2

Hence, the value of y is defined only if y is positive,

But y is a real number

Hence, if y is negative, there is not corresponding element of x

i.e; for y=-1 , there is no value of x in A. 

Hence, h is not onto.

Hence, h is not bijective.

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

CBSE Board exams twice a year from 2025, no plan for semesters: MoE
anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question