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Provide solution for RD Sharma Maths Class 12 Chapter Functions Exercise 2.2 Question 5.

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Answer : f\; o\; g (2)=633

              g\; o\; f (1)=2188

Hint :g\; o\; f means f(x) function is in g(x) function

         f\; o\; g means g(x) function is in f(x) function

Given : f:R\rightarrow R ; f(x)=x^{2}+8

             g:R\rightarrow R ; g(x)=3x^{3}+1

Solution :

First, we find f\; o\; g

           f\; o\; g(x)=f(g(x))=f(3x^{3}+1)

           f\; o\; g(x)=(3x^{3}+1)^{2}+8                                                           \because [(a+b)^{2}=a^{2}+b^{2}+2ab]

          f\; o\; g(2)=(3\times(2)^{3}+1)^{2}+8

                             =\left ( 3 \times 8+1 \right )^{2}+8



f\; o\; g(2)=633


g\; o\; f(x)=g(f(x))=g(x^{2}+8)=3(x^{2}+8)^{3}+1

g\; o\; f(1)=3(1+8)^{3}+1\Rightarrow 3(9)^{3}+1

                   =3\times 729+1


Hence, f\; o\; g(2)=633 \; \text {and} \; g\; o\; f(1)=2188

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