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### 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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