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Please solve RD Sharma Class 12 Chapter Functions Exercise 2.3 Question 1 Sub question (iii) maths textbook solution.

Answers (1)

Answer :

$\begin{aligned} &f \circ g(x)=|\sin x| \\ &g \circ f(x)=\sin |x| \end{aligned}$

Hint : The Range of $f=(0,\infty )$ $f=(0,\infty )\; \subset$ domain $g(R)$

$\Rightarrow \; \; \; \; \; g\; o\; f$ exists

And Range of $g=[-1,1]\subset$ domain R

$\Rightarrow \; \; \; \; \; \; f\; o\; g$ exists

Given : Here given that

$f(x)=\left | x \right |\; \text {and}\; g(x)=\sin x$

Here we have to find out $f\; o\; g$ and $g\; o\; f$

Solution :

First , we will find out $f\; o\; g(x)$

$\begin{aligned} f \circ g(x) &=f\{g(x)\} \\ &=f\{\sin x\} \\ &=|\sin x| \end{aligned}$

Again, we find out $g\; o\; f(x)$

$\begin{aligned} g \circ f(x) &=g\{f(x)\} \\ &=g\{|x|\} \\ &=\sin |x| \end{aligned}$

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