and 
are inverse functions
if 
Calculus
Lesson
28
Inverse Functions
Back to Dr. Nandor's Calculus Notes Page
Back to Dr. Nandor's Calculus Page
and are inverse functions
if
for all 
in the
domains of both 
and
.
The notation is 
and
Example: if 
then
as long as 
(you don't know how to find 
yet,
but we can test
to make sure that it is true!)
Example: if 
then
as long as 
has an inverse iff it
is 1-1. That is, it must be a function and it must be
monotonic (it must pass both the horizontal and vertical line tests).
Plot 
to show
that 
has an
inverse and 
does not.
Steps to finding inverse functions:
1) does 
even have an inverse?
2) rewrite 
as 
and solve 
for 
.
3) interchange 
and 
.
4) check that 
5) domain and
range of 
must be the
same as range and domain of 
Examples: 
(check domain/range for
each!!)
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Finally, note that 
(slopes
are NOT perpendicular, but related)