I can imagine having to refer to these notes regularly, so I'm putting them here!
- 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:
- Determine image set of .
- Invert to find a unique in the domain of .
(all same as above for finding an image set)
gives a unique soluition in , hence has a unique inverse rule: