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

Answers (1)

Answer :

\begin{aligned} &f \circ g(x)=2 x+4 \\ &g \circ f(x)=2 x+5 \end{aligned}

Hint : Domain f \circ g=\{x: x \in R \text { and } 2 x+3 \in R\}

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

Given : Here given that

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

Solution :

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

Here, f: R \rightarrow R, g: R \rightarrow R

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

\begin{aligned} \Rightarrow \quad f \circ g: R \rightarrow R & \\ f \circ g(x) &=f\{g(x)\} \\ &=f(2 x+3) \\ &=2 x+3+1 \\ &=2 x+4 \end{aligned}

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

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

\begin{aligned} \Rightarrow \quad f \circ g: R \rightarrow R \\ g \circ f(x) &=g\{f(x)\} \\ &=g(x+1) \\ &=2(x+1)+3 \\ &=2 x+5 . \end{aligned}

Hence, f \circ g(x)=2 x+4 \text { and } g \circ f(x)=2 x+5

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