(0,1)
[0,12)
[0,1]
[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.As →1,x1+x→12Hence , the range off(x) is[0,12)