The following moves are performed on g(x).(i) Pick (x0, y0) on g(x) and travel toward the left/right to reach the y = x line. Now travel above/below to reach g(x). Call this point on g(x) as (x1, y1)(ii) Let the new position of (x0, y0)be (x0, y1)This is performed for all points on g(x) and a new function is got. Again these steps may be repeated on new function and another function is obtained. It is observed that, of all the functions got, at a certain point (i.e. after finite number of moves) the nth derivatives of the intermediate function are constant, and the curve passes through the origin. Then which of the following functions could be g(x)

• A. y = \(\sqrt{1 – x^2}\)
• B. xy3⁄2 + y = constant
• C. x9 y3⁄2 + y6 x3⁄2 = constant
• D. x7 y 8 + 4y = constant