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Question

Let f(x)=x[x]1+x[x],x ϵ R, where [ x] denotes the greatest integer function. Then, the range of f is

A
(0,1)
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B
[0,12)
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C
[0,1]
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D
[0,12]
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Solution

The correct option is B [0,12)
The graph of y=x[x] is as shown below


When x is an integer, x[x]=0
Hence, f(x) = 0 when x is an integer
x[x] as x tends to an integer.
Let X = x[x]
So, f(x)=X1+X,X ϵ [0,1)
As X1,X1+X12
Hence, the range of f(x) is [0,12) .

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