### Combining Functions

Package of problems

## Problem

Part of the definition of a function is the specification of its domain. The choice of domain may affect the range of the function.

What is the largest possible domain for each of the functions $A$ to $D$ and what is the corresponding range?

The functions above have been composed in some way to make the following new functions:

Can you work out which functions have been composed and in what order to make the new functions?

What are the domain and range for each composition of functions above?

Note that the composition might only be defined on a smaller domain than is possible for the function $f(x)$.