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Provide solution for RD Sharma Maths Class 12 Chapter Functions Exercise 2.2 Question 4.

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Answer : g\; o\; f=\left \{ (a,a),(b,b),(c,c) \right \}\; \text {and}

               f\; o\; g=\left \{ (u,u),(v,v),(w,w) \right \}

Hint : For any function to be a bijective, the given function should be one-one and onto.\

Given : A=\left \{ a,b,c \right \}

             B=\left \{ u,v,w \right \}

Solution :

f and g be two functions from A to B and from B to A ; A\rightarrow B\; \text {and}\; g:B\rightarrow A

                     f=\left \{ (a,v),(b,u),(c,w) \right \}f=\left \{ (a,v),(b,u),(c,w)\right \}

                     g=\left \{ (u,b),(v,a),(w,c)\right \}

For both f and g, Different elements of the domain have different images.

                   \therefore f and f are onto

Again, for each element in co-domain of f and g, there in a preimage in domain

                    \therefore f and f are onto

Thus,              f and g are bijectives.


          g\; o\; f=\left \{ (a,a),(b,b),(c,c) \right \} \text {and}

          f\; o\; g=\left \{ (u,u),(v,v),(w,w) \right \}

Hence prove, f and g both are bijections

g\; o\; f=\left \{ (a,a),(b,b),(c,c) \right \}\; \text {and} f\; o\; g=\left \{ (u,u),(v,v),(w,w) \right \}

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