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Question

The solution set of the inequation ||x|2|<|2x|,xR is

A
ϕ
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B
(,0)
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C
(,2)(2,)
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D
(,2)
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Solution

The correct option is B (,0)
||x|2|<|2x|,xR
Let f(x)=||x|2| and g(x)=|2x|
f(x)=|2|x||
f(x)={|2x| ,x0|2+x| ,x<0


So, f(x)=g(x) x0
and f(x)<g(x) x<0
Hence, required solution is x(,0)

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