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

Answers (1)

Answer :

\begin{aligned} &f \circ g(x)=C \\ &g \circ f(x)=\sin C^{2} \end{aligned}

Hint : The range of g is a subset of the domain of f .

Given: Here given that

             f(x)=C \text { and } g(x)=\sin x^{2}

Here we have to compute f\; o\; gand g\; o\; f.

Solution :

First , we will compute the f\; o\; g

We have, f \circ g: R \rightarrow R

                               \begin{aligned} f \circ g(x) &=f\{g(x)\} \\ &=f\left(\sin x^{2}\right) \\ &=C \end{aligned}

Now we will compute g\; o\; f

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

\begin{aligned} \Rightarrow \quad f \circ g: R & \rightarrow R \\ g \circ f(x) &=g\{f(x)\} \\ &=g(C) \\ &=\sin C^{2} \end{aligned}

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