1 / 11

SECTION 4.1

SECTION 4.1. COMPOSITE FUNCTIONS. COMPOSITION:. A pit crew for a race car driver had a formula for the distance the car had traveled as a function of time: d(t). And they had a formula for the amount of fuel left in the car as a function of the distance traveled: f(d).

dagan
Download Presentation

SECTION 4.1

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. SECTION 4.1 • COMPOSITE FUNCTIONS

  2. COMPOSITION: • A pit crew for a race car driver had a formula for the distance the car had traveled as a function of time: • d(t)

  3. And they had a formula for the amount of fuel left in the car as a function of the distance traveled: f(d)

  4. By hooking the two functions together in an operation called composition, the pit crew can obtain a formula for the amount of fuel remaining in the car as a function of time: • (f  d) (t) or f ( d ( t ) )

  5. EXAMPLE: • Let f(x ) = x 2 - 1 and g(x) = 1/x • Calculate (f  g)(2) and (g  f)(2) f(g(2)) f(1/2) (1/2)2 - 1 -3/4 g(f(2)) g(3) 1/3

  6. f(x ) = x 2 - 1 and g(x) = 1/x • Write formulas for (f  g) (x) and (g  f) (x) and determine their domains. g(f(x)) f(g(x)) ( 1/x )2 - 1 1/x2 - 1

  7. COMPOSITIONS AND THEIR DOMAINS DO EXAMPLES 3 AND 4

  8. WHEN TWO COMPOSITIONS ARE EQUAL DO EXAMPLE 5

  9. DECOMPOSING FUNCTIONS Let F(x) = (x 4 - 2) 3 Decompose F(x) as two functions. Let f(x) = x 4 - 2 and g(x) = x 3 Then F(x) = (g  f) (x)

  10. F(x) = (x 4 - 2) 3 Decompose F(x) as three functions. Let f(x) = x 3 , g(x) = x - 2 , h(x) = x 4 Then F(x) = f(g(h(x)))

  11. CONCLUSION OF SECTION 4.1

More Related