Composition and Decomposition

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!