Inverses and One-to-One Functions

Let’s consider the following two functions.

Source: U.S. Postal Service

Suppose we reverse the arrows. Are these inverse relations functions?

Source: U.S. Postal Service

We see that the inverse of the postage function is not a function. Like all functions, each input in the postage function has exactly one output. However, the output for 2009, 2010, and 2011 is 44. Thus in the inverse of the postage function, the input 44 has three outputs, 2009, 2010, and 2011. When two or more inputs of a function have the ...

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