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  • Provide solution for RD Sharma maths Class 12 Chapter Functions Exercise 2.3 Question 12 maths text book solution.

Provide solution for RD Sharma maths Class 12 Chapter Functions Exercise 2.3 Question 12 maths text book solution.

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Answer :

f \circ f(x)=\left\{\begin{array}{ll} 2+x ; & 0 \leq x \leq 1 \\ 2-x ; & 1<x \leq 2 \\ 4-x ; & 2<x \leq 3 \end{array}\right.

Hint : Range of f=[0,3] \subseteq \text { domain of } f.

Given : Given that  f(x)=\left\{\begin{array}{cc} 1+x ; & 0 \leq x \leq 2 \\ 3-x ; & 2 \leq x \leq 3 \end{array}\right.

Here we have find out f\; o\; f

Solution :

We have,

              Range of \mathrm{f}=[0,3] \subseteq \text { domain of } \mathrm{f}

\begin{aligned} &\therefore f \circ f(x)=\mathrm{f}(\mathrm{f}(\mathrm{x})) \\ &=\mathrm{f}\left\{\begin{array}{cl} 1+\mathrm{x} ; & 0 \leq x \leq 2 \\ 3-\mathrm{x} ; & 2 \leq x \leq 3 \end{array}\right. \\ &\Rightarrow f \circ f(x)=\left\{\begin{array}{cl} 2+x ; & 0 \leq x \leq 1 \\ 2-x ; & 1 \leq x \leq 2 \\ 4-x ; & 2 \leq x \leq 3 \end{array}\right. \end{aligned}

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