Math 2341, Solutions to Homework No. 1
1. Let f : X V , g : X V and h : X V be functions from X to V , and let a, b K. Now
O : X V is given by O(x) = 0 for all x X. For all x X, we have
(f + (g + h)(x) = f (x) + (g + h)(x) = f (x) + (g(x) + h(x)
= (f (x)