First remember that raising a quantity to a fractional exponent is equivalent to taking the radical of the number in the exponent's denominator.

Therefore, we can rewrite the expression as g(x) = ∜(2x-3) + 1

Thus, because taking an even root of any negative results in a non-real or imaginary number, we know that 2x - 3 must be ≥ 0.

Solve the inequality by adding 3 to each side and then dividing by 2 to find that the domain of g(x) is x ≥ 3/2, which is choice C.