1 / 14

Composition of Functions Section 1-8

Composition of Functions Section 1-8. Objectives. I can find the composition of one function with another function. Function Composition. Notation. This does not say “FOG”. You read this “f of g of x”. Function Composition. Notation. Another way to write this is. OR f[g(x)].

kineks
Download Presentation

Composition of Functions Section 1-8

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. Composition of FunctionsSection 1-8

  2. Objectives • I can find the composition of one function with another function

  3. Function Composition Notation This does not say “FOG” You read this “f of g of x”

  4. Function Composition Notation Another way to write this is OR f[g(x)]

  5. Function Composition Notation

  6. Function Composition OR EX 1: f(x) = x2 g(x) = x + 1 Start with g(x) and put that in to f(x) = (x + 1)2 = x2 + 2x + 1

  7. Function Composition EX 2: f(x) = x + 2g(x) = 4 – x2 Start with g(x) and put that in to f(x) = (4 – x2)+ 2 = -x2 + 6

  8. Function Composition EX 3: f(x) = x2 +1 g(x) = 2x Start with g(x) and put that in to f(x) = (2x)2+ 1 = 4x2 + 1

  9. evaluating with Function Composition EX 4: f(x) = x2 +1 g(x) = 2x Start with g(x) & find g(3). Put that answer in to f(x). g(3) = 6 f(6) = 37

  10. MORE Function Composition EX 5: f(x) = x2 - 4 g(x) = 4x - 1 • f[g(-1)] • g(f(2)) • f[g(a + 1)] g(-1) = -5; f(-5) = 21 f(2) = 0;g(0) = -1 g(a+1)= 4(a+1)-1 = 4a+3; f(4a+3) = (4a+3)2 – 4 = 16a2+24a+5

  11. MORE Function Composition EX 5: f(x) = x2 - 4 g(x) = 4x - 1 • d) [f o g](x) g(x) = 4x – 1 so put this into f(x) for x (4x – 1)2 - 4 16x2 – 8x - 3

  12. MORE Function Composition EX 6: f(x) = |x| g(x) = x3 - 2 • [f o g](x) • (g o f)(x) • (f o g)(-2) |x3 – 2| |x|3 - 2 10

  13. 7) For what values of “x” isf(g(x)) = 10 Given: f(x) = 2x and g(x) = x + 3 Start from the outside. Set f(x); 2x = 10 and solve. Check by seeing if: f(g(2)) = 10 So x = 5. This means that g(x) = 5. x + 3 = 5; therefore x = 2

  14. Homework • WS 2-2

More Related