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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 $f\; o\; g$

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

$=f(x^{3})$

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

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

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