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Let `C_1C_2` be the graphs of the functions `y=x^2` and `y=2x ,` respectively, where `0lt=xlt=1.` Let `C_3` be the graph of a function `y=f(x),` where `0lt=xlt=1, f(0) =0.` For a point `P` on `C_1,` let the lines through `P ,` parallel to the axis, meet `C_2` and `C_3` at `Q` and `R ,` respectively (see Figure). If for every position of `P(onC_1),` the areas of the shaded regions `OPQ` and `ORP` are equal, determine the function `f(x)`

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