Find two functions h, k: R rightarrow R such that neither h nor k is a constant map, but k o h is a constant map. Solution Consider the following two functions: h(x) = x - [x] k(x) = [x] Where [x] is the biggest integer less than or equal to x. It\'s obvious that h and k are not constant functions. We have: x-1 < [x] <= x Therefore: 0 <= x - [x] < 1 So for all values of x: 0 <= h(x) < 1 So we have: koh = k(h(x)) = [h(x)] and because 0 <= h(x) < 1 : [h(x)] = 0 Thus k(h(x)) = [h(x)] = 0 Therefore koh is a constant function..