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Please solve RD Sharma Class 12 Chapter Functions Exercise 2.3 Question 10 maths textbook solution.

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Answer :

\begin{aligned} &(f \circ g)(x)=\sqrt{x^{2}+4} \\ &(g \circ f)(x)=x+4 \end{aligned}

Given : Here given that

            f(x)=\sqrt{x+3} \text { and } g(x)=x^{2}+1

Here we have to find out f\; \circ \; g and g\; \circ \; f

Solution :

First, we will compute f\; \circ \; g

                                   \begin{aligned} (f \circ g)(x) &=f(g(x)) \\ &=f\left(x^{2}+1\right) \\ &=\sqrt{x^{2}+1+3} \\ (f \circ g)(x) &=\sqrt{x^{2}+4} \end{aligned}

Again, we will compute g\; \circ \; f

                                     \begin{aligned} (g \circ f)(x) &=g(f(x)) \\ &=g(\sqrt{x+3}) \\ &=(\sqrt{x+3})^{2}+1 \\ (g \circ f)(x) &=x+4 \end{aligned}

Hence, (f \circ g)(x)=\sqrt{x^{2}+4} \text { and }(g \circ f)(x)=x+4

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