I can imagine having to refer to these notes regularly, so I'm putting them here!

# Image Sets

- State the domain of .
- Rearrange so is a function of (to discover the condition under which remains valid.

e.g., for :

# Domain of Combined Functions

Domain of combined functions are the intersection () of the domains of all component functions and that of the combined function. e.g:

# Domain of Composite Functions

For and with domains and respectively, the domain of is:

e.g., for:

# Inverses

- Determine image set of .
- Invert to find a unique in the domain of .

For

(all same as above for finding an image set)

gives a unique soluition in , hence has a unique inverse rule: