Combinations of Functions

Objective: In this lesson you learned how to find arithmetic
combinations and compositions of functions.

I. Arithmetic Combinations of Functions (Pages 229-230)

Just as two real numbers can be combined with arithmetic
operations , two functions can be combined by the operations of

to create new functions. A combined function like this is called
an arithmetic combination of functions.

The domain of an arithmetic combination of functions f and g
consists of . . .

Let f and g be two functions with overlapping domains.
Complete the following arithmetic combinations of f and g for all
x common to both domains:
1) Sum : ( f + g)(x) =
2) Difference : ( f - g)(x) =
3) Product : ( fg)(x) =
4) Quotient:

Example 1:
Let f (x) = 7x - 5 and g(x) = 3 - 2x . Find
( f - g)(4) .
 

II. Composition of Functions (Pages 231-232)

The composition of the function f with the function g is defined
as ( f o g)(x) =

For the composition of the function f with g, the domain of
( f o g) is . . .

For two functions f and g, to find ( f o g)(x) , . . .

Example 2:
Let f (x) = 3x + 4 and let g(x) = 2x² -1. Find
(a) ( f o g)(x) and (b) (g o f )(x) .

III. Applications of Combinations of Functions (Page 233)

The function f (x) = 0.06x represents the sales tax owed on a
purchase with a price tag of x dollars and the function
g(x) = 0.75x represents the sale price of an item with a price tag
of x dollars during a 25% off sale. Using one of the combinations
of functions discussed in this section, write the function that
represents the sales tax owed on an item with a price tag of x
dollars during a 25% off sale.

Additional notes