1. Do Now:

2. 5.5: Perform Function Operations
Algebra II
5.5: Perform Function Operations

3. Operations on Functions
You have learned how to add, subtract, multiply, and divide polynomial expressions. These operations can also be defined for functions.

4. Operations on Functions
Definition
Addition
(f+g)(x) = f(x)+g(x)
Subtraction
(f – g)(x) = f(x) – g(x)
Multiplication
(fg)(x) =
Division

5. Example 1

6. Example 2
Let f(x) = 3x3 – 2x2 + 5 and g(x) = x3 – 3x2 + 4x – 2 . Find (f – g)(x) and state the domain. Then evaluate the difference when x = -2.

7. Addition and Subtraction
Let f(x) = x+5 and g(x) = x2 – 5x + 2
Find f(x) + g(x)
Let f(x) = -3x1/3 + 4x1/2 and
g(x) = 5x1/3 + 4x1/2
Find f(x) – g(x)

8. Example 3

9. Example 4

10. Multiplication and Division
Let f(x) = 4x2/3 and g(x) = 5x1/2
Find g(x) . f(x)
Find g(x)/f(x)

11. Do Now: f(x)=4x1/2, g(x)=-9x1/2, h(x)=6x, m(x)=x3/4 f(x) + g(x)
h(x)m(x)
h(x)/m(x)

12. Composition of Functions
Find the following:
f(0) = g(0) =
f(1) = g(1) =
f(20) = g(20) =
Think:
f(g(x)) g(f(x))

13. Composition of Functions
The composition of a function g with a function f is: h(x) = g(f(x))

14. Perform the indicated operation.
Let f(x) = 2x2 and g(x) = 3x – 5
Find g(f(x))
Find f(g(x))

15. Find the indicated value.
Let f(x) = 4x + 7 and g(x) = 12x – 1
Find g(f(3))
Find f(g(3))

16. Find the indicated value.
Let g(x) = -x2 and h(x) =
Find h(h(-4))
Find g(h(8))

17. Perform the indicated operation.
Let f(x) = 2x2 – x , g(x) = , and
h(x) =
Find f(g(x))

18. Perform the indicated operation.
Let f(x) = 2x2 – x , g(x) = , and
h(x) =
Find g(h(x))

19. Perform the indicated operation.
Let f(x) = 2x2 – x , g(x) = , and
h(x) =
Find f(h(x))