1 / 7

Composite Functions

Composite Functions. Example 1: Given functions f ( x ) = x 2 – 3 x and g ( x ) = 2 x + 1, find f  g. The notation " f  g " means f ( g ( x )). In other words, replace x in function f with 2 x + 1 (the g function). f ( x ) = ( x ) 2 – 3( x ).

umay
Download Presentation

Composite 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. Composite Functions Example 1: Given functions f(x) = x2 – 3x and g(x) = 2x + 1, find f g. The notation "f g" means f (g(x)). In other words, replace x in function f with 2x + 1 (the g function). f (x ) = (x)2 – 3(x)

  2. Composite Functions Example 1: Given functions f(x) = x2 – 3x and g(x) = 2x + 1, find f g. The notation "f g" means f (g(x)). In other words, replace x in function f with 2x + 1 (the g function). f (x ) = ( )2 – 3( ) = f (g(x)) = (2x + 1)2 – 3(2x + 1) f g f  g= 4x2 + 4x + 1 – 6x – 3 f  g= 4x2 – 2x – 2

  3. Example 2: Given functions and find f g and state its domain. x x Composite Functions Simplify the complex fraction by multiplying the numerator and denominator by x + 1.

  4. Composite Functions At first glance it might appear that the domain of f g is the set of all real numbers except - 1.5.

  5. However, remember that the g function, replaced x in the f function. Therefore, the domain of f g is: ( - , - 1.5 )  ( - 1.5, - 1 )  ( - 1,  ). Composite Functions Since the g function is not defined for x = - 1, neither is the f g function.

  6. Try: Given functions and find f g and state its domain. The composite function, f g = x. Its domain is: [ - 5,  ). Composite Functions

  7. Composite Functions END OF PRESENTATION

More Related