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Chapter 10
Compositions, Inverses, and
Combinations of Functions
10.1 Composition of Functions
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View Full Document Key Points
•
Finding the composition of two functions
numerically, graphically and symbolically
•
Interpreting the composition of two
functions
•
Decomposing a function
Formulas for Composite Functions
Example 1
Let
p
(
x
) = cos
x
+ 1 and
q
(
x
) =
x
2
+ 2.
a.
Find a formula in terms of
x
for
r
(
x
) =
p
(
q
(
x
)).
b.
Find a formula
s
(
x
) =
p(q(q(x
)).
c.
Find a formula
t
(
x
) =
q
(
p
(
x
)).
Functions Modeling
Change:
A Preparation
for Calculus,
4th
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View Full Document Decomposition of Functions
Example 4
Let
h
(
x
) =
f
(
g
(
x
)) =
. Find possible formulas for
f
(
x
) and
g
(
x
).
Functions Modeling
Change:
A Preparation
for Calculus,
4th
1
2
+
x
e
22,36,52,54
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•
The function
f
(
g
(
t
)) is said to be a
composition
of
f
with
g
.
•
The function
f
(
g
(
t
)) is defined by
using the output of the function
g
as
the input to
f
.
•
The function
f
(
g
(
t
)) is only defined for
values in the domain of
g
whose
g
(
t
)
values are in the domain of
f
.
•
The function
f
(
g
(
t
)) is said to be a
composition
of
f
with
g
.
•
The function
f
(
g
(
t
)) is defined by
using the output of the function
g
as
the input to
f
.
•
The function
f
(
g
(
t
)) is only defined for
values in the domain of
g
whose
g
(
t
)
values are in the domain of
f
.
Functions Modeling
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This note was uploaded on 04/04/2012 for the course MATH 2412 taught by Professor Staff during the Spring '08 term at Austin CC.
 Spring '08
 Staff

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