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

Answers (1)

Answer : $f\; o\; g=\left | x \right | \; \text {and} \; g\; o\; f=\left | x \right |$

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 : $f(x)=x$

$g(x)=\left | x \right |$

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, $g\; o\; f (x)=g(f(x))$

$=g(x)$

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

Similarly ,

$f\; o\; f (x)=f(g(x))$

$=f \left | x \right |$

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

Hence, $f\; o\; g= \left | x \right |\; \text {and}\; g\; o\; f=\left | x \right |$

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