# 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)

What you should learn How to add , subtract , multiply , and divide functions |

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)

What you should learn How to find the composition of one function with another function |

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) = 2x^{2} -1. Find

(a) ( f o g)(x) and (b) (g o f )(x) .

I**II. Applications of Combinations of Functions**
(Page 233)

What you should learn How to use combinations of functions to model and solve real -life problems |

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.

Homework AssignmentPage(s) Exercises |

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