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Composition of Functions
Hauen laguntzarekin: Smith
Input:
   3
Plus 10
A FUNCTION rule changes
 an INPUT to an OUTPUT
Output:
   13
Input:
   7
Plus 10
A FUNCTION rule changes
 an INPUT to an OUTPUT
Output:
  
Input:
   64
Plus 10
A FUNCTION rule changes
 an INPUT to an OUTPUT
Output:
  
Input:
   x
Plus 10
An input doesn't have to
be a number.  Unknown inputs
are often represented by "x"
Output:
  x+10
Input:
   x
Plus 4
Write the OUTPUT
expression (no spaces)
Output:
 
Input:
   x
Plus 4
HIT OK
Output:
 
x+4
Original Input

g's output

Composition of functions:
    2 functions in a row.


Is placed into f
Composition output
Original Input
?
g's output
?
Composition of functions:
    2 functions in a row.


Is placed into f
?
Composition output
?
The result of g( )
 is sent thru f( )

It can be written as:
 f[g(x)] OR: (f ο g)(x)
Either way, the function
in the MIDDLE goes 1st


Find  (f ο g)(x)

     f[g(x)]
Given that:

g(x) = 2x "double the input"
f(x) = x+1 "input plus one"
g
?
2x
f
?
x+1
Given that:

g(x) = 2x "double the input"
f(x) = x+1 "input plus one"


Find  (f ο g)(x)

     f[g(x)]
g
x
2x
f
x+1
2x
?
2x+1
?
Given that:

g(x) = 2x "double the input"
f(x) = x+1 "input plus one"
Numeric Inputs
are even easier:

Find  (f ο g)(6)

     f[g(6)]
g
6
2x
f
x+1
12
?
13
?
Given that:

g(x) = 2x "double the input"
f(x) = x+1 "input plus one"
Numeric Inputs
are even easier:

Find  (f ο g)(7)

     f[g(7)]
g
7
2x
f
x+1
Fill in the
OUTPUTS
Given that:

g(x) = 2x "double the input"
f(x) = x+1 "input plus one"
Numeric Inputs
are even easier:

Find  (f ο g)(-3)

     f[g(-3)]
g
2x
f
x+1
Fill in the
BLANKS
If f(x) = x -5 and
if g(x) = x2
Which function
is performed 1st?

Find  (g ο f)(8)

    
f, input minus 5
g, input squared
If f(x) = x -5 and
if g(x) = x2

Find  (g ο f)(8)

    
f
x-5
g
Fill in the
BLANKS
x2

Find  (f ο g)(-7)

    
If f(x) = x -5
if g(x) = x2
Which function
is performed 1st?
f, input minus 5
g, input squared
functions

Find  (f ο g)(-7)

    
If f(x) = x -5
if g(x) = x2
function g
is in the middle,
it goes first
g
-7
?
x2
?
f
?
x-5
?
Phil Lynn
DaBlanx

Find  (f ο g)(-7)

    
If f(x) = x -5
if g(x) = x2
g
-7
x2
f
x-5
Check ALL composite functions that appy function f 1st
The function in the MIDDLE goes first
(f ο g) (-6)
(g ο f) (-6)
f[g(-6)]
g[f(-6)]
Check ALL composite functions that appy function g 1st
The function in the MIDDLE goes first
(f ο g) (-6)
(g ο f) (-6)
g
f[g(-6)]
g[f(-6)]
f
Dirty
Clothes
?
Laundry Composite
Function Machine
Clean,
  wet
Clothes
?
Dry, clean
Clothes
?
(ball)
The
End
⊜
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