Section 1.7 Combinations of Functions; Composite Functions
The Domain of a Function
possible values for x
Finding a Function’s Domain
Watch for function’s that model data – real life may impose some restrictions (i.e. no negative
distances)
Cannot divide by zero
Cannot take even root of a negative number
EX 1:
Let the function
9
14
.
0
)
(
+

=
x
x
C
, represent the millions of cars sold x years after 1990.
(Because of production of the type of vehicles changed back to a focus on cars in 2004 this data is only
good through the year 2003.)
Find the domain of
C(x).
EX 2:
Find the domain of each function:
a.)
17
3
)
(
2

+
=
x
x
x
f
b.)
9
3
)
(
2

=
x
x
x
g
c.)
16
2
)
(

=
x
x
h
The Algebra of Functions
1.) Sum:
)
(
)
(
)
)(
(
x
g
x
f
x
g
f
+
=
+
2.)
Difference:
)
(
)
(
)
)(
(
x
g
x
f
x
g
f

=

3.)
Product:
)
(
)
(
)
)(
(
x
g
x
f
x
fg
⋅
=
4.)
Quotient:
0
)
(
,
)
(
)
(
)
(
≠
=
x
g
if
x
g
x
f
x
g
f
EX 3:
Let
5
)
(

=
x
x
f
and
1
)
(
2

=
x
x
g
.
Find each of the following functions:
a.)
)
)(
(
x
g
f
+
b.)
)
)(
(
x
g
f

c.)
)
)(
(
x
fg
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d.)
)
(
x
g
f
EX 4:
Let
3
)
(

=
x
x
f
and
1
)
(
+
=
x
x
g
.
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 Fall '08
 Mcbride,V
 Composite Functions, ex, Injective function

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