Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma Class 12 Chapter Functions Exercise 2.2 Question 14 maths textbook solution.

Explain solution RD Sharma Class 12 Chapter Functions Exercise 2.2 Question 14 maths textbook solution.

Answers (1)

Answer : g\; o\; f is an onto function

Hint : Onto function means every range has some pre-image in the domain of function.

Given : f:A\rightarrow B\; \text {and}\; g:B\rightarrow C are onto function

Prove : g\; o\; f:A\rightarrow C is an onto function

Solution :

Let y\; \epsilon \; C then

       \begin{aligned} &g \circ f(x)=y \\ &g(f(x))=y \end{aligned}                                             ....(i)

Since,  g is onto, for each element in C, then exists a pre-image in B.         

        g(x)=y                                                   .....(ii)   

From (i) and (ii)

       f(x)=x

Since    f  is onto, for each element in B, there exist a pre image in A     

      f(x)=x                                                       ....(iii)

From (ii) and (iii)  we can conclude that for each y\; \epsilon \; C, there exist a preimage in A

Such that g\; o\; f(x)=y

g\; o\; f is onto.

Posted by

infoexpert23

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