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 \[x\in R,\,\,|x|\,=\,\left\{ \begin{matrix} x, & x\ge 0 \\ -x, & x<0 \\ \end{matrix} \right.\] |
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.You need to login to perform this action.
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