Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Show that the function f in <img alt="A= R-\left \{ \frac{2}{3} \right \}\, defined\: as\: f\left ( x \right )= \frac{4x+3}{6x-4}" src="https://entrancecorner.codecogs.com/gif.latex?A%3D%20R-%5Cleft%20%5C%7B%20%5Cfrac%7B2%7D%7B3%7D%20%5Cright%20%5

Show that the function f in A= R-\left \{ \frac{2}{3} \right \}\, defined\: as\: f\left ( x \right )= \frac{4x+3}{6x-4}  is one-one and onto. Hence .find f^{-1}\cdot

 

 

 

 
 
 
 
 

Answers (1)

Let \alpha ,\beta \; \epsilon A\; \; and\; \; f\left ( \alpha \right )= f\left ( \beta \right )
\therefore \frac{4\alpha +3}{6\alpha -4}= \frac{4\beta +3}{6\beta -4}
\Rightarrow 24\alpha \beta -16\alpha +18\beta -12= 24\alpha \beta -16\beta +18\alpha -12
\Rightarrow \alpha = \beta  so f is one-one
Let y\epsilon A  such that  y= \frac{4x+3}{6x-4}
\Rightarrow 6xy-4y= 4x+3\; \Rightarrow\; 6xy-4x= 4y+3
\Rightarrow x= \frac{4y+3}{6y-4}\: \epsilon A  for all y\, \epsilon \, A  so f is onto
\therefore f^{-1}\left ( y \right )= \frac{4y+3}{6y-4}\; or\; f^{-1}\left ( x \right )= \frac{4x+3}{6x-4}

Posted by

Ravindra Pindel

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 question papers QR codes part of 'internal systems'; board cautions 'unverified claims'
anam-khan

Delhi court grants interim bail to Class 12 student in stabbing case to appear for CBSE exam
anam-khan

CBSE Class 12 History Exam 2026 Analysis: Moderate paper, tricky MCQs, student-friendly pattern

Latest Question