1 / 9

IGCSE Revision Lesson 7

IGCSE Revision Lesson 7. I can use function notation , e.g. f (x) = 3x- 5, f:x--> 3x- 5 to describe simple functions, I can form composite functions as defined by gf(x) = g(f(x)) I can use the notation f -1 (x) to describe their inverses , which I can subsequently find.

mimis
Download Presentation

IGCSE Revision Lesson 7

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. IGCSE Revision Lesson 7 • I can use function notation, e.g. f (x) = 3x- 5, f:x--> 3x- 5 to describe simple functions, • I can form composite functions as defined by gf(x) = g(f(x)) • I can use the notation f -1(x) to describe their inverses, which I can subsequently find

  2. IGCSE Revision Lesson 7 f(x) means “some function applied to x” e.g. f(x) = 3x + 2 f(2) = f(4) = f(-1)=

  3. IGCSE Revision Lesson 7 Notice the difference: f(x) = 3x + 2 f(2) = f(x) = 5, x = We are working backwards. “When you do ‘f’ to x, the answer is 5. What is x?’

  4. IGCSE Revision Lesson 7 • We also have f(x) = 3x + 2 f -1(4) = f -1 (x) =

  5. IGCSE Revision Lesson 7 e.g. g(x) = 4(x – 5) g(1) = g(x) = 16 g -1(20) = g -1(x) = 2 What equivalent statements can we make for these?

  6. This notation can also be used in graphs...

  7. IGCSE Revision Lesson 7 f(x) = x2 + 2 g(x) = 3x – 1 fg(x) = gf(x) = Read as f(g(x)) Read as g(f(x)) fg(x) = f(3x – 1) gf(x) = g(x2 + 2) = (3x – 1)2 + 2 = 3(x2 + 2) -1 = 9x2 – 6x + 1 + 2 = 3x2 + 6 – 1 = 9x2 – 6x + 3 = 3x2 + 5

  8. IGCSE Revision Lesson 7 fg(x) = gf(x) = gh(x) = ff(x) =

  9. Inverse – working the other way. e.g. f(x) = 3x – 2 Method 1: Flow diagram What does f(x) tell us to do to x? Method 2: Change the terms x = input, let y = output Inverse means we switch the input and output... then solve. y = 3x – 2  x = 3y – 2 x + 2 = 3y x + 2 = y 3 IGCSE Revision Lesson 7 • Method 2: Change the terms x = input, let y = output Inverse means we switch the input and output... then solve. y = 3x – 2  x = 3y – 2 x + 2 = 3y x + 2 = y 3 x 3 - 2 x 3x 3x - 2 ÷ 3 + 2 x + 2 x + 2 x 3

More Related