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: