Unformatted text preview: Inverse Functions
Inverse
Section 3.6 Graphs of Inverse Relations
Graphs Let f be a function. If (a, b) is a point o the
Let
(a,
graph of f, then (b, a) is a point o the graph
of its inverse.
of The graph of the inverse of f is a reflection of
The
the graph of f across the line y = x. OnetoOne Functions
OnetoOne A function f is onetoone if f(a) = f(b)
iimplies that a = b.
mplies
b. If a function is onetoone, then its
If
inverse is also a function.
inverse Use the horizontal line test to determine if
Use
a function is onetoone
function Not onetoone Onetoone Composition of Inverse
Functions
Functions A onetoone function f and its inverse function f −1
onetoone
have these properties.
have
f −1 o f ) ( x) = x (
( f o f ) ( x) = x
−1 for every x in the domain of f.
for
f −1
for every x in the domain of Also, any two functions having both properties are
onetoone and are inverses of each other.
onetoone Joke Time
Joke What’s a cow’s favorite
What’s
painting?
painting?
The Moona Lisa What does the tooth fairy give
for half a tooth?
for
Nothing. She wants the tooth,
Nothing.
the whole tooth, and nothing
but the tooth!
but ...
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This note was uploaded on 12/01/2011 for the course MATH 111 taught by Professor Stuff during the Winter '11 term at BYU.
 Winter '11
 stuff
 Calculus, Inverse Functions

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