M5.1.1 For the adult
Domain, range and inverses
Can I put any number into a function, and can every number come out?
What this chapter teaches
The domain is the set of inputs a function allows, and the range is the set of outputs it gives. A function has an inverse only when different inputs always give different outputs. Restricting the domain can make this true. The inverse swaps x and y, so its graph is the mirror image in the line y = x.
Three questions to ask
There is no one right wording. Listen for the idea.
- What numbers can you not put into 1/(x − 3), and why?
- Why does x² have no inverse on all real numbers, and how can you mend that?
- If the point (2, 9) is on a graph of f, which point is on the graph of f⁻¹?
After the chapter, the learner can
- Find the domain and range of a function
- Say when a function has an inverse
- Sketch a function and its inverse, mirrored in y = x
What they copy into their notebook
Domain: inputs allowed. Range: outputs reached. Only a one to one function has an inverse; restrict the domain to get one. f⁻¹ swaps x and y, so reflect the graph in y = x.