Let

To find , first, we need to find the inverse of the function . Let’s set , which gives us . Rearranging this equation to solve for in terms of yields .

Now to find , we substitute into our inverse function:

.

So, .

Now let’s add some additional fun knowledge!
Did you know that inverses can often be visualized as reflections across the line ? When you plot and its inverse on the same graph, you’ll see this delightful symmetry which showcases the beautiful relationship between functions and their inverses!

Also, this method of finding the inverse function isn’t just limited to rational functions. You can use this approach for a variety of functions, making it a powerful tool for solving equations and understanding relationships in algebra! Just remember to check that your function is one-to-one, or else you’ll need to restrict the domain!