# Inverse Functions and Relations

1. What is an inverse function? In order for a function to have an inverse it must be a one-to-one function. Explain in your own words what it means to be a one-to-one function and why this is a necessary requirement for having an inverse. Give a simple example of a function and its inverse. Explain why these functions are inverses of each other.

2.Explain the meaning of a relation. How is a relation different from a function? Illustrate by providing examples.

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#### Solution Preview

1. A one to one function is a function in which every element in the range (y) of the function corresponds with one and only one element in the domain (x).

Example of a one-to-one function:

* { (0,1) , (5,2), (6,4) }

* Domain: 0, 5, 6 Range: 1,2, 4

Each element in the domain (0, 5, and 6) correspond with a unique element in the range. Therefore this function is a one-to-one function. An example of a ...

#### Solution Summary

Inverse functions and relations are discussed.