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Sec. 2.6 – Operations and Composition
We can combine functions using the operations of addition, subtraction, multiplication,
and division.
Addition of functions :
(
)( )
( )
( )
f
g x
f x
g x
+
=
+
Subtraction of functions :
(
)( )
( )
( )
f
g x
f x
g x

=

Multiplication of functions :
(
)( )
( )
( )
f g x
f x
g x
⋅
=
⋅
Division of functions :
( / )( )
( ) / ( )
f g x
f x
g x
=
Which says to add, subtract, multiply, or divide two functions, we simply add, subtract,
multiply, or divide their individual function rules. Or for a particular value of x, we
simply add, subtract, multiply, or divide the related range values.
Ex.
( )
2
3
f x
x
=

and
2
( )
2
g x
x
=
+
So (f + g)(x) =
f(x) + g(x)
=
2
(2
3)
(
2)
x
x

+
+
=
2
2
3
2
x
x
 +
+
=
2
2
1
x
x
+

Ex.
To find a particular value’s sum, say (f + g)(5) , we can do it in 2 ways:
1)
Find the combined function (as we did above), and then substitute the value , 5,
for x in the combined function.
2
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 Spring '10
 stean

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