Do Now:

If f(x) = 4x2 – 3,
1.Find f(-3)
2.Find the inverse of the
function
Focus Question: How
can we evaluate
composite functions?
December 17, 2013
Composite Functions
 Take
the answer you get from one
function and put it into the other
function.
 Written as:
1. f(g(x)) or (f o g)(x)
 Evaluate
g(x) and then put that answer into f(x)
2. g(f(x)) or
 Evaluate
(g
o
f)(x)
f(x) and then put that answer into g(x)
 These 2 are NOT the same!
f(x) = 4x
g(x) = 5x - 3
1. Evaluate (fog)(3)

g(3) = 5(3) – 3
= 12
2. Evaluate (gof)(3)


f(12) = 4(12)
= 48
 (fog)(3) = 48


f(3) = 4(3) = 12
g(12) = 5(12) – 3
= 57
(gof)(3) = 57
Notice: They are not the same answer!
f(x) = 3x + 6
g(x) = x2 - 4
3. Evaluate f(g(-4))

g(-4) = (-4)2 – 4
= 16 – 4
= 12
4. Evaluate g(f(-2))



f(12) = 3(12) + 6
= 42
f(-2) = 3(-2) + 6
=0
g(0) = (0)2 – 4
= -4
f(x) = ⅔ x
g(x) = x2 – 3x + 5
5. Evaluate (fog)(-4)


g(-4) = (-4)2 – 3(-4) + 5
= 16 + 12 + 5
= 33
f(33) =
⅔
6. Eval (gof)(-9)

= 22
⅔
(-9)
= -6

(33)
f(-9) =
g(-6) = (-6)2 – 3(-6) + 5
= 36 + 18 + 5
= 59
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
f(x) = 4x
g(x) = 5x - 3
1. Find (fog)(x)
2. Find (gof)(x)
 f(g(x))
 g(f(x))
f(5x-3)
3)
12
=
= 4(5x –
= 20x –
= g(4x)
= 5(4x) – 3
= 20x – 3
ORDER is important!
f(x) = x2 – 2x + 3
g(x) = x + 3
3. Find f(g(x))
 f(g(x))
3
+3
= f(x + 3)
= (x + 3)2 – 2(x+3) +
= x2 + 6x + 9 – 2x – 6
= x2 + 4x + 6
f(x) = x2 - 4 g(x) = 3x + 6
4. Find (g
o
f)(x)
g(x2 – 4) = 3(x2 – 4) + 6
= 3x2 – 12 + 6
= 3x2 – 6
Summary
 Composite
functions are:
– Easy if you’re careful
– Compound functions
– Taking the answer from one function &
putting it into the other function