If x≥0, then [x] is an integer part of x. Hence x2≥[x]2 and f(x)=√x2−[x]2 is well-defined. If x<0 say x=− a where a is a positive number, then [x]=−([a]+1) Hence, x2<[x]2 and the function f(x)=√x2−[x]2 is not defined. Therefore the domain of the function is [0,∞).