As we are learning more about functions, you are probably noticing more and more relationships in your daily life as well as your work, that do represent functions. In this module, we are learning about a new class of functions which are special, as they are invertible. These functions are very useful! You may not have realized this before, but it is because inverse functions that we can actually solve equations! When we solve an equation like x + 6 = 8 we realize that by subtracting 6 from both sides of the equation we get x by itself, to find x = 2. What property did we just apply?

Well we use the fact that the inverse of adding 6 is subtracting 6. That is, a function and its inverse composed together "undo" each other. Another way of thinking of invertible functions is whether they are reversible or not. For example, the process of burning a paper is not reversible, since you can't take ash and put it back together into a paper. So, the process of burning paper is not reversible. However, boiling water is a process that is reversible. Can you think of why?

For this module discussion, think about processes in your life that are functions. You can look back to Module 2 where you introduced a function for ideas. Describe the function and determine if it is invertible or not. Explain why or why not.