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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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