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
169
Example
: Let
( )
5
f x
x
=
−
and
2
( )
2
g x
x
=
−
. Find:
(a) (
)(4)
f
g
=
D
(b) (
)(9)
g
f
=
D
(c) Find the composite functions and their domains
(
)( )
g
f
x
=
D
Domain:

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