What is the domain of f(x)= sqr|x|-x

If you mean the square root of the absolute value of x minus x, that is f(x) = sqrt( |x| ) - x, then the domain is R, that is all the real numbers. However, if you meant the square root of x minus x, that is f(x) = sqrt(x) - x, then the domain is [0, infinity).

Since we take modulus in sqr so x can be any real number.
So Domain's Real set R.

Domain's Real set R.

x belongs to R