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Provide solution for RD Sharma Class 12 Chapter Functions Exercise 2.3 Question 1 Sub question (vi) maths textbook solution.

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Answer :

\begin{aligned} &g \circ f(x)=\sin (x+1) \\ &f \circ g(x)=\sin x+1 \end{aligned}

Hint : f: R \rightarrow R ; g: R \rightarrow[-1,1]

Given : Here given that

            f(x)=x+1\; \text {and}\; g(x)=\sin x

            we have  to compute f\; o\; g (x) and g\; o\; f (x)

Solution :

First, we have to compute f\; o\; g

Clearly, the range of g is a subset of the domain f.

Set of the domain of f.

\Rightarrow \; \; \; \; \; \; f\; o\; g:R\rightarrow R

                                        \\ f\; o\; g (x)=f\left \{ g(x) \right \}

                                                           =f(\sin x)

                                                           = \sin (x+1)

Now, we will compute g\; o\; f

                                       g\; o\; f (n)=g\left \{ f(n) \right \}

                                                          =g\left \{ x+1 \right \}

                                                          =\sin (x+1)

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