### Combining Functions

Package of problems

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## Solution

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

To find the domain and range for a function, it sometimes helps to sketch its graph.

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 $f(x)$.