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

Answers (1)

Answer : f\; o\; g = 9x^{2}-18x+5f\; o\; g = 9x^{2}-18x+5\; \text {and}\; g\; o\; f=3x^{2}+6x-13

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(x)=x^{2}+2x-3

            g(x)= 3x-4

Solution :

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

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

Now,  g\; o\; f (x)=g(f(x))=g(x)

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

          g\; o\; f (x)= 3\left ( x^{2}+2x -3\right )-4

          g\; o\; f (x)= 3x^{2}+6x -9-4

          g\; o\; f (x)= 3x^{2}+6x -13

          f\; o\; g (x)= f(g(x))=f(x)

          f\; o\; g (x)= f(g(x))=f \left ( 3x-4 \right )

          f\; o\; g (x)= \left ( 3x-4 \right )^{2}+2\left ( 3x-4 \right )-3

                             =9x^{2}+16-24x+6x-8-3                                            \because \left [ \left ( a-b \right )^{2}=a^{2}+b^{2} -2ab\right ]

         f\; o\; g (x)=9x^{2}-18x+5

Hence, f\; o\; g = 9x^{2}-18x+5\; \text {and}\; g\; o\; f=3x^{2}+6x-13

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