Solution 7.

See text and/or instructor's solution manual.

Solution.   Assume that    is an odd function  (i.e.     for all ).  

      

Therefore,   .  

We are done.   

Aside.  We can look at the result of Exercise 4 to illustrate this fact.

                     The function     satisfies   .   

                     because    is an odd function, i. e.   .   

This solution is complements of the authors.

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