You can encode and decode messages using functions and their inverses. To code a

Chapter 1, Problem 117

(choose chapter or problem)

You can encode and decode messages using functions and their inverses. To code a message, first translate the letters to numbers using 1 for “A,” 2 for “B,” and so on. Use 0 for a space. So, “A ball” becomes

1 0 2 1 12 12.

Then, use a one-to-one function to convert to coded numbers. Using f(x) = 2x − 1, “A ball” becomes

1 −1 3 1 23 23.

(a) Encode “Call me later” using the function f(x) = 5x + 4.

(b) Find the inverse function of f(x) = 5x + 4 and use it to decode 119 44 9 104 4 104 49 69 29.