1. 1.5 Combination of Functions
PreCalculus
1st Semester

2. Objectives: Add, subtract, multiply and divide functions.
Find compositions of one function with another function.
Use combinations of functions to model and solve real life problems.

3. Sum, Difference, Product, and Quotient of Functions
Let f and g be two functions with overlapping domains. Then, for all x common to both domains, the sum, difference, product, and quotient of f and g are defined as follows:
Sum: (f + g)(x) = f(x) + g(x)
Difference (f – g)(x) = f(x) – g(x)
Product (fg)(x) = f(x) g(x)
Quotient

4. Example 1:

5. Example 2:

6. Example 3:

7. Example 4:

8. Composition of Functions
Definition of Composition of Two Functions:
Read as “f of g” of x

9. Example 5:

10. Example 6: