M4.10.2 For the adult
Composite and inverse functions
If I put a number into g, and then put the answer into f, is that the same as doing f first?
What this chapter teaches
A composite function puts one function inside another: fg(x) means f(g(x)), so g works first. The order matters. An inverse function f⁻¹ undoes f. To find it, undo the steps of f in the reverse order. The mark −1 on f does not mean 1 divided by f.
Three questions to ask
There is no one right wording. Listen for the idea.
- In fg(x), which function goes first, and how do you know?
- How do you find the inverse of f(x) = 3x − 2?
- How can you check that you have found the right inverse?
After the chapter, the learner can
- Find fg(x) from two functions f and g
- Find the inverse function f⁻¹(x)
What they copy into their notebook
fg(x) means f(g(x)): g goes first. The order matters. The inverse f⁻¹ undoes f: reverse the steps. Check it by putting a number through f, then f⁻¹.