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Kendra Kilmer January 4, 2012
Section 1.6  Inverse Functions and Logarithms
Definition:
A function
f
is said to be
if each range value corresponds to exactly one domain value.
Horizontal Line Test:
If every horizontal line intersects the graph of a function
f
in no more than one place, then
f
is a onetoone function.
Example 1:
Which of the following functions are onetoone?
Definition:
If
f
is a onetoone function with domain
A
and range
B
, then its
inverse function
f
−
1
has domain
B
and range
A
and is defined by
f
−
1
(
y
) =
x
⇔
f
(
x
) =
y
for any
y
in
B
. Thus, if
(
a
,
b
)
is a point on the graph of
f
, then
(
b
,
a
)
is a point on the graph of
f
−
1
. Thus, if
f
is
onetoone, then the graph of its inverse,
f
−
1
, is a reflection about the line
y
=
x
.
Example 2:
If
f
is a onetoone function and
f
(
5
) =
7 and
f
(
3
) =
4, find
a)
f
−
1
(
7
)
b)
f
(
f
−
1
(
4
))
How to Find the Inverse Function of a OnetoOne Function
f
1. Write
y
=
f
(
x
)
.
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 Fall '08
 Allen
 Inverse Functions

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