In the sketch below, the blue curve is our function f(x). The red curve is the inverse of f(x). How do we know it is the inverse? The blue line and the red line are the respective tangents at point A and point A' (which is the inverse of point A.) Point A is the only point that you can drag.
Questions: 1) What do you notice about the ordered pairs of A and A'? Should this surprise you? 2) The slopes of the tangent lines are given. What is the relationship between the two? Click on the check box to verify your answer. How does that verify your answer? 3) How would you mathematically calculate the slopes of the two tangent lines?