1. 1.5 Combintions of Functions
Students will be able to:
- add, subtract, multiply, and divide functions.
- find compositions of one function with another.
- Use combinations of two functions to model and solve real-life problems.

2. Sum, Difference, Product, and Quotient of Function
Sum: (f+g)(x) = f(x) + g(x)
Difference: (f-g)(x) = f(x) – g(x)
Product: (fg)(x) = f(x)•g(x)
Quotient:

3. Example 1:
Given and , find Then evaluate the sum when x = 2.

4. Example 2:
Given and , find (f – g)(x). Then evaluate the difference when x = 2.

5. Example 3
Given and , find (fg)(x). Then evaluate the product when x = 4.

6. Example 4:
Find (f/g)(x) and (g/f)(x) for the functions given by and Then find the domains of each.

7. Example 5:
Find for , . If possible, find and .

8. Example 6:
Given f(x) = x + 2 and , evaluate (a) and (b) when x = 0,1,2, and 3.

9. Example 7:
Find the domain of the composition for the functions given by and

10. Example 8:
Given and , find each composition.
a. b.

11. Example 9:
Write the function as a composition of two functions.

12. Example 10:
Write the function as a composition of two functions.

13. Composition of Functions:
Convert miles to inches.

14. Example
F(x) displays the percent increase in UV radiation when the ozone layer thins by x% X 1 2 3 4 5 6
F(x)
1.5
4.5
7.5 9
G(x) displays the percent increases in cases of skin cancer given the % increase in UV radiation X
1.5 3
4.5 6
7.5 9
G(x)
5.25
10.5
15.75
21.0
26.25
31.5
G(F(2) =
Describe what G(F(x)) computes.