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)()( xgxf
)()( xgxf
)()( xgxf
)(
)(
xg
xf
2( ) 3 4
( ) 4
f x x
g x
x
x
Function Operations
))(( xgf
( 6
5
)
( ) 2g x
x
x
f x
Composition of Functions
))(( xfg
Composition is not commutative
( ) ( )f x g x 1( ) 1
3
( ) 3 9
g
f x x
x x
You Try!
( ) ( )g x f x
( ( ))f f x
))(( xgf
2( ) 3 4
( ) 4
f x x
g x
x
x
Composition of Functions
))(( xfg
))(( xgf
( 3
1
)
( )g x
f x
x
x
Composition of Functions
( ( ))g g x
Find the indicated values for the following functions if:
2 3f x x
2 1g x x
( (1))f g ( (2))g f
3 34 & 2f x x g x x
1.
2.
3.
4.
f x g x
f x g x
f x g x
f x
g x
6& 3 5f x g x x
x
1. 2
2. 4
3. 3
4. 1
f
g
f
g
5. 2
6. 4
7. 3
8. 1
g f
f g
g f
f g
