Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 7 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 7 Maths Textbook Solution.

Answers (1)

Answer:              

f^{-1}\left ( x \right )=\sqrt{x-4}

Given: 

                f\left ( x \right )=x^{2}+4,f:R\rightarrow R_{+}\rightarrow \left [ 4,\infty \right ].

Hint:

Bijection function should be fulfil the injectivity and surjectivity.

Solution:

Let x,y be two elements of the domain \left ( a \right ).

\! \! \! \! \! \! \! \! \! \! f\left ( x \right )=f\left ( y \right )\\\\x^{2+4}=y^{2}+4\\\\x^{2}=y^{2}\\\\x=y

So fis one-one.

Let  y be in the co-domain\left ( a \right ) such that

                \! \! \! \! \! \! \! \! f\left ( x \right )=y\\\\x^{2}+4=y\\\\x^{2}=y-4\\\\x=\sqrt{y-4}\epsilon \: R

                f is onto, so f is bijection.

                \! \! \! \! \! \! \! \! f^{-1}\left ( x \right )=y\\\\x=f\left ( y \right )\\\\x=y^{2}+4\\\\x-4=y^{2}y=\sqrt{x-4}\\\\f^{-1}\left ( x \right )=\sqrt{x-4}                                                                                                                                       … (i)

               

Posted by

infoexpert27

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