Get Answers to all your Questions

header-bg qa

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)


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


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support