1. 1.2 Composition of Functions
Objectives: Perform operations with functions. Find composite functions. Iterate functions using real numbers.

2. Operations with Functions:
Sum: (f + g)(x) = f(x) + g(x)
Difference: (f – g)(x) = f(x) – g(x)
Product: (f·g)(x) = f(x) · g(x)
Quotient: (f/g)(x) = f(x)/g(x) , g(x) ≠ 0
Given f(x) = 2x – 1 and g(x) = x²-1, find each function.
A) (f + g)(x)
B) (f – g)(x)
C) (f·g)(x)
D) (f/g)(x)
Example 1)

3. Find (f ○ g)(x) and (g ○ f)(x) for f(x) = x² - 1 and g(x) = 3x
Example 2)
For the Lotsa Coffee Shop, the revenue r(x) in dollars from selling x cups of coffee is r(x)=1.5x. The cost c(x) for making and selling the coffee is c(x)=0.2x
Write the profit function and find the profit on 100, 200, and 500 cups of coffee sold.
Given functions f and g, the composition function f ○ g (“f of g”)can be described by
(f ○ g)(x) = f(g(x))
Find (f ○ g)(x) and (g ○ f)(x) for
f(x) = x² - 1 and g(x) = 3x
Composite:
Example 3)

4. *find domain of f(x) and g(x) first
State the domain of f(g(x)) if f(x)=√x-2 and g(x) = 1/4x
*find domain of f(x) and g(x) first
The composition of a function and itself
Find the first three iterates of the function
f(x) = 3x + 2 for an initial value of x=4
Example 4)
Iteration:
Example 5)