Inverse Functions and Gradients



Use the interactivity above to explore different functions and their inverses. Often the method we use to find inverses begins with swapping x and y in the equation. Geometrically this is a reflection in the line y=x which swaps the x and y axes. Is the inverse function always the same as the reflection? If not why not? Enable the tangents and their reflection. What is the numerical relationship between and ?


Can you use the relationship to find derivatives of the following functions? , ,