Inverse functions can be used to send and receive coded information. A simple example might use the function

Suppose that each letter of the alphabet is assigned a numerical value according to its position, as follows.

Using the function, the word ALGEBRA would be encoded as

because

and so on. The message would then be decoded using the inverse of ƒ, which is

and so on. Work Exercises in order.

Suppose that you are an agent for a detective agency. Today’s encoding function is ƒ(x) = 4x - 5. Find the rule for ƒ^-1 algebraically.

f(x) = 2x+5. (Note that it is one-to-one.)