What makes two functions inverses

There are two steps required to evaluate f at a number x. First we multiply x by 3, then we add 2. Thinking of the inverse function as undoing what f did, we must undo these steps in reverse order.

The steps required to evaluate f -1 are to first undo the adding of 2 by subtracting 2. Then we undo multiplication by 3 by dividing by 3. Step 2 often confuses students. We could omit step 2, and solve for x instead of y, but then we would end up with a formula in y instead of x. The formula would be the same, but the variable would be different. To avoid this we simply interchange the roles of x and y before we solve. This is the function we worked with in Exercise 1.

From its graph shown above we see that it does have an inverse. In fact, its inverse was given in Exercise 1. Exercise Find f -1 x. Most of the steps are not all that bad but as mentioned in the process there are a couple of steps that we really need to be careful with since it is easy to make mistakes in those steps. For all the functions that we are going to be looking at in this course if one is true then the other will also be true.

However, there are functions they are beyond the scope of this course however for which it is possible for only one of these to be true. This is brought up because in all the problems here we will be just checking one of them. We just need to always remember that technically we should check both. However, it would be nice to actually start with this since we know what we should get. This will work as a nice verification of the process. Now, we need to verify the results.

Here are the first few steps. Now, be careful with the solution step. With this kind of problem it is very easy to make a mistake here. Okay, this is a mess. That was a lot of work, but it all worked out in the end. To understand more about how we and our advertising partners use cookies or to change your preference and browser settings, please see our Global Privacy Policy. Page 1 of 3. So, just crunching some Algebra, here's one way to look at it: If you're got two functions, f x and g x , and then f x and g x are inverse functions.

So, and Yep, they are inverses, just like we thought! Accept All Cookies.