For numbers smaller than -1, g(x) will have a negative number under the radical sign, will be undefinded for real numbers.
However, f(x), for values less than -1, both the numerator and the denominator will be negative, giving a positive answer, and will then be defined.
The functions will be equaivalent if x > -1; for x ≤ -1, f(x) will be defined but g(x) won't be.