Hello wonderful mathematics people. This is Anna Cox from Kellogg Community College. Inverse functions F of G of X equal X for all X in the domain of G&G of F of X equal X for all X in the domain of F. Then F&G are inverses of each other. The domain of F is the range of G and the range of F is the domain of G Sometimes the notation is a little circle which is our of F of G of X just means FG of X. For a function to have an inverse, it must be 1 to one and the function must pass the horizontal line test. The horizontal line test is just like the vertical line test which we used to determine if the relation was a function. So it means that every horizontal line can only pass through the graph one time. To find the inverse algebraically, we switch the X and the Y and solve for the new Y. The correct notation is F of X&F inverse of X. Thank you and have a wonderful day.