#### Need solution for RD Sharma Maths Class 12 Chapter Function Exercise 2.2 Question 7.

Answer : $\fn_cm f\; o\; g \neq g\; o\; f$

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

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

Given :  $\fn_cm f:R \rightarrow R$ defined by

$\fn_cm f(x)=x^{2}$

$\fn_cm g:R\rightarrow R$ defined by

$\fn_cm g(x)= x+1$

Solution :

$\fn_cm f\; o\; g(x)=f(g(x))=f(x+1)$

$\fn_cm f\; o\; g(x)=(x+1)^{2}$                                               $\fn_cm \therefore [(a+b)^2=a^2+b^2+2ab]$

$\fn_cm f\; o\; g(x)=x^{2}+1+2x$                                                 ......(i)

Similarly,

$\fn_cm g\; o\; f(x)=g(f(x))=g(x^{2})$

$\fn_cm g\; o\; f(x)= x^{2}+1$                                                            .....(ii)

Now we have to make a comparison between eq. (i) and (ii)

$\fn_cm f\; o\; g(x) \neq g\; o\; f(x)$

$\fn_cm x^{2}+1+2x \neq x^{2}+1$

Hence proved $\fn_cm f\; o\; g \neq g\; o\; f$