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Please solve RD Sharma class 12 chapter Functions exercise 2.2 question 1 sub question (ii) maths textbook solution.

Answers (1)

Answer : f\; o\; g=2x^{3}+x^{6}\; \text {and}\; g\; o\; f=\left ( 2x+x^{2} \right )^{3}

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

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

Given : f\left ( x \right )=2x+x^{2}

             g\left ( x \right )=x^{3}

             f:R\rightarrow R\; \text {and}\; g:R\rightarrow R

            f\; o\; g:R\rightarrow R\; \text {and}\; g\; o\; f:R\rightarrow R

Solution :

First, we find g\; o\; f

g\; o\; f\left ( x \right )=g\left ( f\left ( x \right ) \right )

                    =g \left ( 2x+x^{2} \right )

g\; o\; f\left ( x \right )= \left ( 2x+x^{2} \right )^{3}

Then we find f\; o\; g

f\; o\; g \left ( x \right )=f\left ( g\left ( x \right ) \right )


f\; o\; g \left ( x \right )=2x^{3}+x^{6}

Hence, f\; o\; g =2x^{3}+x^{6} and g\; o\; f = \left ( 2x+x^{2} \right )^{3}


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