help please organized your solution (do not cursive)

2.38.) The graph of the equation (x2 + y2 - 2x)2 = x2 + y2 is given in Figure 2.7.6. (a) Use a CAS, or straightforward algebra, to find four functions defined implicitly by this equation. By either method, it might help to start with the substitution Y = y?. (b) Use a graphing utility to obtain the graph of each function. (c) Give the domain of each function found in part (a). 13 FIGURE 2.7.6 Graph for Problem 34[ Algebra Do not jump to the conclusion from the preceding examples that an equation F(x, y) = 0 can readily be solved for y. For example, it is known that the equation - 3xy (9) defines several functions implicitly, but very few instructors of mathematics (including the authors) can solve equation (9) for y without looking up a specialized formula. The graph of the equationx' + y = 3xy shown in FIGURE 2.7.5taj is a famous curve called the Folium of Descartes. With the aid of a computer algebra system (CAS) such as Mathematica or Maple, one of the functions y = f(x) defined implicitly by (9) is found to be 2r yV-48 + 4Vx - 4x V-4r + 4V/x - 4r. x# 0. (10) CHAPTER 2 FUNCTIONS The graph of this function consists of the red ares shown in Figure 2.7.5(b). Note the hole in the red graph at the origin. (a) Folium (b) Function FIGURE 2.7.5 Graph of (9) in (a); Graph of (10) in (b) One last point, solving an equation F(x. y) = 0 for y in terms of x is often more than just an exercise in challenging algebra or a lesson in the use of the correct syn- tax of a CAS. Sometimes it is simply impossible! For example, the equation xtxy-y - 2r-y=0 (11)