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Material Type: Notes; Class: College Algebra; Subject: (Mathematics); University: University of Houston; Term: Unknown 1989;
Typology: Study notes
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Section 3.6 – L3 – Page 1 of 8
Method
Definition
Addition
f^ g^ x
f x
g x
+^
Subtraction
f^ g
x^
f x^
g x
Multiplication
fg^
x^
f x g x =
Division
f^
f^ x x g^
g x ^ ^ ^ ^ ^
Composition
f^ g
x
f^ g x =
D
Section 3.6 – L3 – Page 2 of 8
Example 8:
For the functions
f^ x^
x = −^
and
g^ x
x = −^
, find the
following and simplify:
a.^ (
f^ g
x^
b.^ (
g^ f
x
c.^ (
f^ f
x
d.^
g^ g
x ^
^
^
^
Section 3.6 – L3 – Page 4 of 8
Example 10:
For the functions
f^ x
x =^
and
g^ x
x = +^
, find the
following and simplify:
a.^
f^ g
x^
b.^ (
g^ f
x
c.^ (
f^ f
x
d.^
g^ g
x ^
^
^
^
Section 3.6 – L3 – Page 5 of 8
Example 11:
For the functions
f^ x
x = −^
and
2
( )^
g x
x = −
, find the
following and simplify:
a.^ (
f^ g
b.^ (
g^ f
c.^ (
f^ f
d.^ (
g^ g
Section 3.6 – L3 – Page 7 of 8
Example 13:
For the functions
2
( )^
f^ x
x = −
g^ x
x = +^
, and
h x
x =^
−^ , find the following and simplify: a.^ (
f^ g
h^
x^ = D^ D b.^ (
g^ g
g^
x^ = D^ D
Section 3.6 – L3 – Page 8 of 8
Example 14:
For the functions
2
( )^
f^ x
x = −
g^ x
x = +^
, and
h x
x =^
−^ , find the following and simplify: a.^ (
f^ g
h^
b.^
f^ g
g h ^
^
^
^
