An applet designed to help with visualising inverse functions (A2 Maths, C3). You can input your own function and your attempt at its inverse, and see how it matches with the reflection in . Includes an explanation into why and when we need to restrict the domain/range (i.e. why it doesn't always match the reflection perfectly!)

1) Start with inputting . If you have worked out the inverse correctly, check that the blue and orange graphs match up exactly. Can you explain why this is?
2) Now try . Find the inverse. Why don't the orange and blue graphs match exactly? Write down the domain and range of the inverse. Is there more than one possible way to define the inverse for this function?
3) Now try , , . , and any others that you can think of! For each one, write down the domain and the range of the inverse (orange graph).
4) Can you find any functions that are self-inverse? (i.e. the inverse of is ! You should be able to think of at least three different types of self-inverse functions.