This document discusses composition and decomposition of functions. It provides examples of composing functions by finding f(g(x)) and g(f(x)) for various functions f(x) and g(x). It also gives examples of decomposing a function h(x) into functions f(x) and g(x) such that h(x) = f(g(x)). The document announces there will be a quiz on this material and assigns homework problems for practice.

1. Warm-Up

2. Homework Questions

3. Composition/Decomposition
Ask good questions – you have a
QUIZ today and this stuff is on it!

4. Composition of Functions
 Let and
 Find f(g(x)) and g(f(x))
( ) x
f x e= ( )g x x=

5. Composition of Functions:
 f(x) = x – 2
 g(x) = x2
 Find (f o
g)(2)
 Find (g o
f)(-3)

6. More Composition:
 f(x) = 2x – 3
 g(x) = 4x + 5
 Find (f o
g)(x)
 Find (g o
f)(x)

7. More Composition:
 f(x) = x2
– 1
 g(x) = √x
 Find (f o
g)(x)
 Find (g o
f)(x)

8. More Composition:
 f(x) = 2x + 1
 g(x) = 3x2
 h(x) = –x – 1
 Find f(g(h(x)))
 Find h(g(f(x)))

9. Decomposing Functions
aka – opposite of composition
 For h(x), find f(x) and g(x) such that
h(x) = f(g(x))
4)1(3)1()( 2
++−+= xxxh

10. Decomposing Functions
aka – opposite of composition
 For h(x), find f(x) and g(x) such that
h(x) = f(g(x))
1)( 3
+= xxh

11. QUIZ!
NO TALKING
NO LOOKING AROUND
NO CELL PHONES

12. Homework
 P. 128 (11-20)
 Bring in a 2 pocket folder by Monday!