question_answer

Direction: (Q. Nos. 86) For \[x\in R,\,f(x)\] is defined as\[f(x)\,=\,\left\{ \begin{matrix}    x+1, & 0\le x\le 2  \\    x-4, & x\ge 2  \\ \end{matrix} \right.\] . For \[x\in R,\,\,|x|\,=\,\left\{ \begin{matrix}    x, & x\ge 0  \\    -x, & x<0  \\ \end{matrix} \right.\]

For \[0\le x\le 1,\] the solution set of \[|x|\,f(x)>2\] is

A)  \[\phi \]                                             

B)  \[(0,\,\,1)\]

C)  \[\left[ \frac{1}{2},\,\,\frac{1}{2} \right]\]                           

D)  None of these

Correct Answer: A

Solution :

 For \[0\le x\le 1,\] \[|x|\,\,f(x)>2\,\,\,\Rightarrow \,\,\,x(x+1)>2\] \[\Rightarrow \]               \[{{x}^{2}}+x-2>0\] \[\Rightarrow \]               \[(x+2)\,\,(x-1)\,>0\] \[\Rightarrow \]               \[x\in (-\infty ,\,\,-2)\,\cup (1,\,\,\infty )\] Hence, there is no solution.