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  • Please solve RD Sharma Class 12 Chapter Functions Exercise 2.3 Question 1 Sub question (iv) maths textbook solution.

Please solve RD Sharma Class 12 Chapter Functions Exercise 2.3 Question 1 Sub question (iv) maths textbook solution.

Answers (1)

Answer :

\begin{aligned} &g \circ f(x)=e^{x+1} \\ &f \circ g(x)=e^{x}+1 \end{aligned}

Hint :  The Range of  f = R \; \subset \text {Domain of } f=R

\Rightarrow \; \; \; \; \; \; f\; o\; g exists

Given : Here given that

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

Here we have to find out g \circ f(x)\; \text {and}\; f \circ g(x)

Solution :

First, we will find out  g\; o\; f (x)

We have,

\begin{aligned} g \circ f(x) &=g\{f(x)\} \\ &=g\{(x+1)\} \\ &=e^{x+1} \end{aligned}

And again, we will find out f\; o\; g (x)

\begin{gathered} f \circ g(x)=f\{g(x)\} \mid \\ \; \; \; \; \;\; \; \; =f\left\{e^{x}\right\} \\ \; \; \; \; \; \; \; \; =e^{x}+1 \\ \text { So, } g \circ f(x)=e^{x+1} \text { and } f \circ g(x)=e^{x}+1 \end{gathered}

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