What is a composite function?
- A composite function is where one function is applied after another function
- The ‘output’ of one function will be the ‘input’ of the next one
- Sometimes called function-of-a-function
- A composite function can be denoted
- All of these mean “ of ”
How do I work with composite functions?
- Recognise the notation
- fg(x) means “f of g of x”
- First apply g to x to get
- Then apply f to the previous output to get
- Always start with the function closest to the variable
- is not usually equal to
- fg(x) and gf(x) are generally different but can sometimes be the same
- ff(x) is written as f2(x)
- Inverse functions ff-1(x) = f-1f(x) = x
- Domain and range are important.In fg(x), the ‘output’ (range) of g must be in the domain of f(x), so fg(x) could exist, but gf(x) may not (or not for some values of x).