Algebra II ­ 7.3 (Day 1)
Power functions and Function Operations
Operations on Functions
Let f and g be any two functions. A new function h can be defined by performing andy of the four basic operations (addition, subtraction, multiplication and division on f and g.
Operation
Addition h(x) = f(x) + g(x)
Subtraction
h(x) = f(x) ­ g(x)
Multiplication
h(x) = f(x) g(x)
Division
Example f(x) = 2x g(x) = x+1
Definition
h(x) = 2x + (x+1) = 3x + 1
h(x) = 2x ­ (x+1) = x ­ 1
h(x) = (2x)(x+1) = 2x2 + 2x
h(x) = f(x) g(x)
h(x) = 2x
(x+1)
The domain of h consists of the x­values that are in the domains of both f and g. Additionally, the domain of a quotient does not include x­values for which g(x) = O
Let f(x) = 2­x and g(x) = 3x. Perform the indicated operation and state the domain.
1. f(x) + g(x)
2. f(x) ­ g(x)
____________
_____________
3. g(x) ­ f(x)
_____________
4. f(x) g(x)
_______________
5. g(x)
f(x)
________________
1
Let f(x) = x2 and g(x) = x­3. Perform the indicated operation and state the domain.
6. f(x) + g(x)
8. g(x) + f(x)
7. f(x) ­ g(x)
9. f(x) g(x)
10. g(x)
f(x)
Let f(x) = 3x1/3 and g(x) = 2x1/3. Perform the indicated operation and state the domain.
11. f(x) + g(x)
12. f(x) ­ g(x)
13. f(x) g(x)
Homework: Page: 14. f(x) g(x)
Problems:
2