Problem: One to One and Inverse Functions
Let A = {1,2,3} and B = {a,b,c}, and let f: A → B.
(a) Give an example of a one to one function from A to B (use the given sets A and B above). Briefly explain why your example is a 1-1 (one-to-one) function.
(b) How many one to one functions from A to B are there? Explain.
(c) Using the above sets A and B define a function f-1, for some function f from A to B.
(d) Is the function g: R → R defined by g(n) = (n/2) a one to one function? (Be careful,(n/2) means the ceiling function.) Explain.
Show your all work.