Exercise 6.  Show that     iff  ,  where  c  is a positive real constant.  

Solution 6.

See text and/or instructor's solution manual.

    For   and ,  suppose  .  

Then for any    (or )  we have  

        ,  and  ,  where  .

    Conversely, suppose  .  Since c is a positive real constant, we have  .  

If  ,  then  ,  so  .  

This gives  ,  and we have proven that  .

A similar argument shows  .   Therefore,  .

This solution is complements of the authors.

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