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  • 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.

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