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

Answers (1)

Answer : g\; o\; f \left ( x \right )=4x^{2}+12x+14 \; \text {and}\; f\; o\; g\; =2x^{2}+13

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

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

Given : 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 :

Now first we find  g\; o\; f

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

                   =\left ( 2x+3\right )^{2}+5

g\; o\; f (x)= 4x^{2}+12x+9+5                                                  \because \left [ \left ( a+b \right )^{2}=a^{2}+b^{2}+2ab \right ]

g\; o\; f (x)= 4x^{2}+12x+14

Now we find f\; o\; g

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

f\left ( x^{2}+5 \right )=2\left ( x^{2}+5 \right )+3

f\; o\; g(x)=2x^{2}+13

Hence, f\; o\; g(x)=2x^{2}+13\; \text {and}\; g\; o\; f(x)=4x^{2}+12x+14




Then we find f\; o\; g 

 f\; o\; g (x)=f(g(x))

                   =f\left ( x^{3} \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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