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 …
If the function or its inverse has a stationary point, then …
When you’re asked to think about general statements like these it is often helpful to visualise or sketch some examples.
What types of functions could help you to think about these observations?
Now try to make similar statements about decreasing functions.
What assumptions have you made about the function or its inverse? Have these assumptions affected your statements?
