Functions 1. (12 points) Let A=(1, 2, 4, 6,8) and B=(2, 4, 6,8, 10). Let f : A- B and g : A -> A with f = {(1,2), (2, 8), (4, 10), (6,2), (8,4)} and g = {(1, 1), (2, 6), (4, 8), (6,2), (8,4)} For each of the following compositions, define the function or explain why it is not defined. (a) fog (b) gof (c) f of (d) gog (e) Find f if it exists. If it doesn't, explain why not. (f) Find g if it exists. If it doesn't, explain why not. 2. (8 points) Consider composition of functions. (a) Let A = (1,2,3), f : A - A = {(1,2), (2,2), (3, 1)), and g : A - A = {(1,3), (2, 1), (3,2)). Find gof and fog. (b) Let f and g go from R to R defined as f(x) = Vx and g(x) = x3. Find go f and fog. (c) Let f and g go from Z X Z to Z X Z defined as f(m, n) = (mn, m?) and g(m, n) = (m + 1, m + n). Find go f and fog