Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class12 Chapter Functions exercise 2.1 question 5 sub question (xv)

Provide solution for RD Sharma maths class12 Chapter Functions exercise 2.1 question 5 sub question (xv)

Answers (1)

Bijective

Hint:

f:R \rightarrow R, defined by f(x)=3-4x.

Hint:

Bijective function should be one-one and onto function.

Solution:

Let  

\begin{aligned} &x_{1}, x_{2} \in R \\ &f\left(x_{1}\right)=3-4 x_{1}, f\left(x_{2}\right)=3-4 x_{2} \\ &f\left(x_{1}\right)=f\left(x_{2}\right) \\ &3-4 x_{1}=3-4 x_{2} \\ &x_{1}=x_{2} \end{aligned}

Hence f  is an injective.

Subjection test:

Let 

 \begin{aligned} &y=3-4 x\\ &x=\frac{3-y}{4}\\ &\therefore\\ &\forall y \in R, \exists \frac{3-y}{4} \in R\\ &f\left(\frac{3-y}{4}\right)=3-4\left(\frac{3-4}{4}\right)=y \end{aligned}

\therefore f is onto

Hence, f is 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

CBSE Single Girl Child Scholarship 2024: Registration extended till January 10; eligibility criteria, amount
anam-khan

CBSE wants international boards reined in; letter to education ministry seeks directions for AIU
anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14

Latest Question