1 / 4

1.2 Composition of Functions

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)

lisajbrown
Télécharger la présentation

1.2 Composition of Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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. 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

  4. 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)

More Related