Try to complete the following observations about a function that has an inverse.
If the function is increasing, then its inverse is …
If the function is increasing rapidly, then its inverse is …
What assumptions have you made about the function?
Move point \(A\) to see if the triangles behave as you expect. Do you notice anything else?
Try to complete the following observation about a function that has an inverse.
- If the function or its inverse has a stationary point, then …
Now take a look at this GeoGebra file. What do you think will happen this time if you move point \(A\) along the curve? (You may need to click the reset symbol (top right of the graph) to see the triangles and point \(A\).)
What can you now say about the gradients of functions that have inverses?
