168
L13
Composite Functions; One-to-one Functions;
Inverse Functions
A
composite
function
f
g
D
(read as “
f
composed
with
g
”) is defined by
(
)( )
(
( ))
f
g
x
f g x
=
D
.
The domain of
f
g
D
is the set of all real
x
in the
domain of
g
for which
(
)
g x
is in the domain of
f
.
Example
: Show a diagram for the composite function
(
)( )
(
( ))
f
g
x
f g x
=
D
Similarly we define: (
)( )
(
( ))
g
f
x
g f x
=
D

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