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) =   a one to one function?  (Be careful,   means the ceiling function.)  Explain.

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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.

means the ceiling function.) Explain.

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