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,∞).