Let f(x)=x−[x]1+x−[x],xϵR, 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,Xϵ[0,1)
As X→1,X1+X→12
Hence, the range of f(x) is [0,12) .