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

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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