Composition of Functions

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Thursday
Last
Day for Test
corrections
Retest 7:40am
tomorrow
Thursday:
Factor these 3 problems
27 x  8
3
9 x  36 x  4 x  16
3
x  81
4
2
Factor these 3 problems
27 x  8
3
(3x  2)(9 x  6 x  4)
2
Factor these 3 problems
9 x  36 x  4 x  16
3
2
(3x  2)(3x  2)( x  4)
Factor these 3 problems
x  81
4
( x  9)( x  3)( x  3)
2
Composition of Functions
Section 1-8
Objectives

I can find the composition of one
function with another function
Function
Composition
Notation
( f g )( x)
This does not say “FOG”
You read this “f composed with
g of x”
Function Composition
Notation
( f g )( x)
Another way to write this
is
f ( g ( x))
OR
f[g(x)]
Function Composition
Notation
( f g )( x)
INSIDE function 1st
OUTSIDE function last
Function Composition
( f g )( x) OR f ( g ( x))
EX 1: f(x) = x2
Start with g(x)
and put that
in to f(x)
g(x) = x + 1
= (x + 1)2
= x2 + 2x + 1
Function Composition
( f g )( x)
EX 2: f(x) = x + 2 g(x) = 4 – x2
Start with g(x)
and put that
in to f(x)
= (4 – x2) + 2
= -x2 + 6
Function Composition
( f g )( x)
EX 3: f(x) = x2 + 1
Start with g(x)
and put that
in to f(x)
g(x) = 2x
= (2x)2 + 1
= 4x2 + 1
evaluating with
Function Composition (Numbers)
( f g )(3)
EX 4: f(x) = x2 + 1
Start with g(x)
& find g(3). Put
that answer in
to f(x).
g(x) = 2x
g(3) = 6
f(6) = 37
MORE
Function Composition
EX 5: f(x) = x2 - 4
g(x) = 4x - 1
a) f[g(-1)] g(-1) = -5; f(-5) = 21
b) g(f(2))
f(2) = 0; g(0) = -1
c) f[g(a + 1)]
g(a+1)= 4(a+1)-1 = 4a+3;
f(4a+3) = (4a+3)2 – 4 = 16a2+24a+5
MORE
Function Composition
EX 5: f(x) = x2 - 4
g(x) = 4x - 1
d) [f o g](x)
g(x) = 4x – 1 so put this into f(x) for x
(4x – 1)2 - 4
16x2 – 8x - 3
6) For what values of “x” is
f(g(x)) = 10
Given:
f(x) = 2x and g(x) = x + 3
Start from the outside.
Set f(x); 2x = 10 and
solve.
So x = 5.
This means that g(x) = 5.
x + 3 = 5; therefore x = 2
Check by
seeing if:
f(g(2)) = 10
Homework

WS 2-4