1. 4-2 Operations on Functions
Homework: Pages , #1, 3, 5-10, 17-19, 23-26, 33, 35
Just like real numbers, you can add subtract, multiply, and divide functions to create NEW functions.
Let f and g be two functions with overlapping domains. Then for all x common to both domains:

2. Sum Example
TI-84?

3. Difference Example
TI-84?

4. Product Example
TI-84?

5. Quotient Example

6. Composition
Composition Example

7. More Composition

8. Doublecheck: Finding the Domain of a Composition

9. Do you remember this special case? What does it mean?
If f(g(x)) = g(f(x)) = x, then the two functions are inverses of each other! Graphically, the functions are symmetric about the line y = x.

10. Decomposing?
In calculus, it will become important to be able to identify two functions that make up a given composite function. Basically, to “decompose” a composite function, look for an “inner” and an “outer” function.
h(x) = (3x – 5)3
f(x) = x3
g(x) = 3x – 5
h(x) = f(g(x))

11. You Try It!

12. Who does this stuff?