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Need solution for RD Sharma Class 12 Chapter Functions Exercise 2.3 Question 2 maths textbook solution.

Answers (1)


Given : Here given that

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

To prove : We have to prove that f \circ g \neq g \circ f

Solution :

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

For f\; o\; g

\begin{aligned} f \circ g(x)=& f(g(x)) \\ &=f(\sin x) \\ &=\sin ^{2} x+\sin x+1 \end{aligned}                                       ...(i)

And now for g\; o\; f

\begin{aligned} g \circ f(x)=& g(f(x)) \\ &=g\left(x^{2}+x+1\right) \\ &=\sin \left(x^{2}+x+1\right) \end{aligned}                                         ... (ii)

From enq. (1) and (2) we proved that

f \circ g \neq g \circ f

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