A) \[[-3,3]\cup (-\infty ,-4)\cup (4,\infty )\]
B) \[(-\infty ,-4)\cup (4,\infty )\]
C) \[(-\infty ,-3)\cup (4,\infty )\]
D) \[(-\infty ,-3)\cup (3,\infty )\]
E) \[[-3,3]\cup (4,\infty )\]
Correct Answer: A
Solution :
Given, \[\frac{3-|x|}{4-|x|}\ge 0\] \[\Rightarrow \] \[3-|x|\le 0\]and\[4-|x|<0\] Or \[3-|x|\ge 0\]and\[4-|x|>0\] \[\Rightarrow \] \[|x|\ge 3\]and\[|x|>4\] Or \[|x|\le 3\]and\[|x|<4\] \[\Rightarrow \] \[|x|>4\]or\[|x|\le 3\] \[\Rightarrow \] \[(-\infty ,-4)\cup [-3,3]\cup (4,\infty )\]
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