Exercise 3.  If f and g are entire functions, which of the following are necessarily entire?   

3 (c).  .

Solution 3 (c).

See text and/or instructor's solution manual.

Solution.    is entire provided that    for all  z,  because    exists for all  z.

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

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