# Question of the Week 8: Domain and Range of Inverse Functions

The following question is taken from my website Diagnostic Questions. Here you will find 1000s of high quality maths multiple choice diagnostic / hinge questions, ideal for assessment for learning, which have been created and shared by maths teachers all over the world.

I have chosen this particular question as Question of the Week this week not because I wrote it (although I think it is a pretty good question, if I do say so myself…), but because it highlights the point that using software and other website can really add a new dimension to questions.

I created this particular question using the outstanding Desmos – a free on line graphing package. I have been using Desmos loads recently with my Year 11 – 13 students as they can have it with them at their desks on their phones and tablets, so when we are investigating quadratic functions, straight line graphs, domain and range, or whatever it might be, they can make a prediction and then immediately test it out for themselves.

Using dynamic websites like Desmos to create Diagnostic Maths Questions also brings with it another huge benefit. If you save the original graph file, you can investigate the question further.

Here is the graph I used to create the above question:

And here is a link to the full Desmos page itself

So, after my students have given their responses to the hinge question, I can delve deeper into the topic, asking questions such as:

• What is the domain of the inverse function?
• Describe the features of the inverse function
• Can you come and sketch the inverse function?
• Can you suggest an equation for the original function?
• What would happen if I change the upper bound of the domain of the original function to 5?

The possibilities are endless!

If you think of ways to combine other websites or software with Diagnostic Questions, please create a question on the website and give me a shout! 🙂