Let C1 and C2 be the graphs of functions y = x2 and y = 2x, 0 ≤ x ≤ 1 respectively. Let C3 be the graph of a function y = f(x), 0 ≤ x ≤ 1, f(0) = 0. For a point P on C1, let the lines through P, parallel to the axes, meet C2 and
C3 at Q and R respectively (see figure). If for every position of P(on C1) the areas of the shaded regions OPQ and ORP are equal, determine the function f(x).