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

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

Answers (1)

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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