1 / 15

Don’t be fooled!!!! You DO NOT get 50% off…

If there is a 40% off sale at Kohl’s and you receive an extra 10% with your mom’s coupon, how much will you pay for a $250 jacket?. Don’t be fooled!!!! You DO NOT get 50% off…. This is an example of a _____ function. ● Since you get 40% off, you will pay 60% of the original price.

hisa
Download Presentation

Don’t be fooled!!!! You DO NOT get 50% off…

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. If there is a 40% off sale at Kohl’s and you receive an extra 10% with your mom’s coupon, how much will you pay for a $250 jacket? Don’t be fooled!!!! You DO NOT get 50% off…

  2. This is an example of a _____ function. ● Since you get 40% off, you will pay 60% of the original price. ● Since you get an additional 10% off of that, you will pay 90% of that price. ● So what are the two equations? g(x) = .9x f(x) = .6x

  3. We put the two together in a COMPOSITE function that looks like this: g(f(x)) Alternate notation: (g○ f)(x) • So to solve g(f(250))… f(x) = .6x g(x) = .9x • First find f(250)  f(250) = .6(250) = 150 • 2. Then compute g(150) = .9(150) = 135

  4. Multiply by 5 Multiply by 5 Add 3 Add 3 Consider the functions: x x 5x x + 3 Think of x going through two “function machines.”To find g(f(x)) – start with f(x)!! x 5(x+3) x + 3

  5. FINAL ANSWER g(f(x)) = 5x + 15

  6. Example: Show that f(g(x)) = 96x-48 f(x) = 12x,g(x) = 8x – 4 I’ll show you how I want you to write it, showing your steps to receive maximum credit!

  7. You try these! If f(x) = 3 – x and g(x) = 4x, (a) Find (i) (f ○ g)(1) (ii) (g ○ f)(5) (b) Show that (g ○ f)(x) = 12 - 4x (c) Find (f ○ g)(3x2)

  8. The Identity Function • You plug in x, and you get x right back out! i(x) = x OR i : x  x Example:Show that f ○ g = i.

  9. Inverse FunctionsThe inverse function, f-1, undoes whatever f does. • So if f is an “add 3 machine” – then what is f-1? • If f is a multiply by 5 machine, what is f-1?

  10. How to find the inverse algebraically. • Example 1: Find the inverse of f(x) = 7x + 2 Now you try it! If f(x) = 4 – 3x, (a) find f-1(x) (b) show that (i) f○f-1 = i (ii) f-1○f= i

  11. **Be sure to include the restricted domain of the inverse if necessary so that it is a function!!! Example: f(x) = x2.Find the inverse, and state the domain so that the inverse function is defined.

  12. Sample IB Question • What you need to know: ln = natural logarithm – the same laws apply to ln as to log. The inverse of ln(x) is ex. • Let f(x) = ln (x+5) + ln (2), for x > -5 • Find f-1(x). Let g(x) = ex (b) Find (gof)(x), giving your answer in the form ax + b

  13. IB Question 2 The functions f(x) and g(x) are defined by f(x) = ex and g(x) = ln(1+2x). (a) Write down f-1(x). (b) (i) Find f ( g ( x )). (ii) Find (f o g)-1(x)

  14. Graphing Inverses On your calculator, graph each of the following pairs of inverses and see if you can determine the relationship between an inverse and its graph. • f(x) = 7x + 2 f-1(x) = 1/7 (x – 2) • f(x) = x2 + 3, x ≥ 0 f-1(x) = √x - 3, x ≥ 3 • f(x) = x1/3 + 2 f-1(x) = (x – 2)3

  15. Homework Assignment • Book p. 97 #1j-l, 2a-c, 3-4 p. 101-102 #1a-e, 7, 9

More Related