Inverse Functions and Gradients
- Author:
- Richard Trimble
- Topic:
- Functions
Explore
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 ?
Challenge
Can you use the relationship
to find derivatives of the following functions?
, ,