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Learn to perform operations with functions, find composite functions, and iterate functions using real numbers. Explore sum, difference, product, and quotient of functions. Practice with examples and iterate functions.
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1.2 Composition of Functions Objectives: Perform operations with functions. Find composite functions. Iterate functions using real numbers.
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)
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 + 110. • 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) http://www.youtube.com/watch?v=zl5QodAFuVk
Example 4) • 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 Iteration: Example 5)
