Direction: (Q. Nos. 87) 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) \[(4,\,\,\infty )\]
B) \[(-\,\infty ,\,\,3)\]
C) \[[3,\,\,4]\]
D) None of these
Correct Answer: C
Solution :
\[\left\{ f(x)+|x-2| \right\}\,f(x)\,\le 0\] \[\Rightarrow \] \[(x-4+x-2)\,(x-4)\le 0\] \[\Rightarrow \] \[2(x-3)\,(x-4)\le 0\] \[\Rightarrow \] \[3\le x\le 4\]You need to login to perform this action.
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