Problem #6 (15 points) Let X = {1, 2, 3). Y = {1, 2, 3, 4). and Z = {1, 2}. Using arrow diagrams, define the functions below. In each case provide a small comment explaining why the required property is true or false. a) Define a function fi: X - Y that is one-to-one but not onto. b) Define a function 2: XZ that is onto but not one-to-one. c) Define a function /: XXthat is neither one-to-one nor onto. d) Define a function fa: X X that is one-to-one and onto but is not the identity function on X. Problem #7 (10 points) Find a function f for which 25(x) 31(-x)= 5x - 1. Problem #8 Consider the functions defined by the diagram alongside a) Find g 1 ( ggf , and flog! b) What is the relationship between (g) and flog