f(x)= [[x]] is the "greatest integer" function. The range of f(x)= x-[[x]] is:

Answer 1

Since [[x]] is the greatest integer that is less than or equal to x we have that [[x]] less than or equal to x < [[x]]+1. So we have that 0 less than or equal to x-[[x]] <1. Thus, the range of your function is [0,1).