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Question

f(x)=2{x}23{x}+1,x[1,1], where [] denotes the fractional part of x. Domain of the function f(x) is:

A
[1,12][0,12]{1}
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B
[1,12][0,12]{2}
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C
[1,13][0,13]{3}
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D
None of these
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Solution

The correct option is A [1,12][0,12]{1}
For f to be defined 2{x}23{x}+10
({x}1)(2{x}1)0
{x}(,12)[1,)
But we know, {x}[0,1)
Thus {x}[0,12)(1)
Also given that x[1,1]
Hence required domain is [1,12][0,12],{1}
Note {x}=1{x}

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