Solution 3 (b).

See text and/or instructor's solution manual.

Use the inverse     and write

                         

Now substitute      and      in the formula      from part (a) and get

                    .  

This can be simplified using the steps  

                    ,    and  

                    ,    and  

                    .  

It is now easy to see that   .  

Therefore, the solution is the line  

                    ,     

that passes through the origin.  

We are done.   

Aside.  We can let Mathematica double check our work.

We are really done.   

Aside.  We can explore some graphs.

                    The image of the circle     under the mapping   

                        is the line        that passes through the origin.   

                    The image of the circle     under the mapping   

                        is the line        that passes through the origin.   

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell