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

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

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 defined by


           g:R\rightarrow R defined by

           g(x)= x+1

Solution :

       f\; o\; g(x)=f(g(x))=f(x+1)

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

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


     g\; o\; f(x)=g(f(x))=g(x^{2})

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

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

     f\; o\; g(x) \neq g\; o\; f(x)

     x^{2}+1+2x \neq x^{2}+1

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

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