Let `C_1 and C_2`, be the graph of the functions `y= x^2 and y= 2x, 0<=x<= 1` respectively. Let `C_3`, be the graph of a function `y- (fx), 0<=x<=1, f(0)=0`. For a point Pand `C_2`, let the lines through P, parallel to the axes, meet `C_2 and C_3`, at Q and R respectively. If for every position of P (on `C_1`), the areas of the shaded regions `OPQ and ORP` are equal, determine the function `f(x)`.

Let C_(1) and C_(2) be the graphs of the functions y=x^(2) and y=2x, respectively, where 0le x le 1." Let "C_(3) be the graph of a function y=f(x), where 0lexle1, f(0)=0. For a point P on C_(1), let the lines through P, parallel to the axes, meet C_(2) and C_(3) at Q and R, respectively (see figure). If for every position of P(on C_(1)), the areas of the shaded regions OPQ and ORP are equal, determine the function f(x).

Let C_(1) and C_(2) be the graphs of the functions y=x^(2) and y=2x, respectively, where 0le x le 1." Let "C_(3) be the graph of a function y=f(x), where 0lexle1, f(0)=0. For a point P on C_(1), let the lines through P, parallel to the axes, meet C_(2) and C_(3) at Q and R, respectively (see figure). If for every position of P(on C_(1)), the areas of the shaded regions OPQ and ORP are equal, determine the function f(x).

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)

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)

Graph the function xy-y-x-2=0 .

Sketch the graph of the function y=2|x-2|-|x+1|+x.

If the graph of the function y=(a-b)^(2)x^(2)+2(a+b-2c)x+1(AA a ne b)

Let C_1 and C_2 be two circles whose equations are x^2+y^2-2x=0 and x^2+y^2+2x=0 and P(lambda, lambda) is a variable point

Let C_(1) and C_(2) be two circles whose equations are x^(2)+y^(2)-2x=0 and x^(2)+y^(2)+2x=0 and P(lambda,lambda) is a variable point