A) \[\left\{ \begin{matrix} x+1-2\le x\le 0 \\ x-10<x\le 2 \\ \end{matrix} \right.\]
B) \[\left\{ \begin{matrix} x-1-2\le x\le 0 \\ x+10<x\le 2 \\ \end{matrix} \right.\]
C) \[\left\{ \begin{matrix} -1-x-2\le x\le 0 \\ x-10<x\le 2 \\ \end{matrix} \right.\]
D) None of these
Correct Answer: D
Solution :
[d] \[(fog)(x)=\left\{ \begin{matrix} f(x+3),1\le x+3\le 2 \\ f(-x+1),-1\le x+2\le 2 \\ \end{matrix} \right.\] \[=\left\{ \begin{matrix} \begin{align} & f(x+3),1\le x+3\le 2 \\ & f(-x+1),\,-1\le -x+1\le 1 \\ \end{align} \\ f(-x+1),\,1\le -x+1\le 2 \\ \end{matrix} \right.\] \[=\left\{ \begin{matrix} \begin{align} & x+1,-2\le x\le -1 \\ & -x-1,\,-1\le x\le 0 \\ \end{align} \\ x-1,\,0\le x\le 2 \\ \end{matrix} \right.\]You need to login to perform this action.
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