Unformatted text preview: Inverse Functions
Section 3.6 Graphs of Inverse Relations
Graphs Let f be a function. If (a, b) is a point o the
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 graph of f across the line y = x. One-to-One Functions
One-to-One A function f is one-to-one if f(a) = f(b)
iimplies that a = b.
b. If a function is one-to-one, then its
inverse is also a function.
inverse Use the horizontal line test to determine if
a function is one-to-one
function Not one-to-one One-to-one Composition of Inverse
Functions A one-to-one function f and its inverse function f −1
have these properties.
f −1 o f ) ( x) = x (
( f o f ) ( x) = x
−1 for every x in the domain of f.
for every x in the domain of Also, any two functions having both properties are
one-to-one and are inverses of each other.
one-to-one Joke Time
Joke What’s a cow’s favorite
The Moona Lisa What does the tooth fairy give
for half a tooth?
Nothing. She wants the tooth,
the whole tooth, and nothing
but the tooth!
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