Objective: Find inverse functions. Warm up 1. a.Find (f o g)(x). b.Find the domain of f(g(x)).

Slides:

Advertisements

Similar presentations

Domain: 1) f(0) = 8 2) f(3) = 3) g(-2) = -2 4) g(2) = 0 5) f(g(0)) = f(2) =0 6) f(g(-2)) = f(-2) =undefined 7) f(g(2)) = f(0) =8 8) f(g(-1)) = f(1) =3.

Advertisements

6.7 Notes – Inverse Functions. Notice how the x-y values are reversed for the original function and the reflected functions.

7.4 Inverse Functions p Review from chapter 2 Relation – a mapping of input values (x-values) onto output values (y-values). Here are 3 ways to.

Functions Domain and range The domain of a function f(x) is the set of all possible x values. (the input values) The range of a function f(x) is the set.

Today in Pre-Calculus Go over homework questions Notes: Inverse functions Homework.

2.7: Use Absolute Value Functions and Transformations HW: p.127 (4-20 even)

Chapter 7 7.6: Function Operations. Function Operations.

Inverse Functions Given 2 functions, f(x) & g(x), if f(g(x))=x AND g(f(x))=x, then f(x) & g(x) are inverses of each other. Symbols: f -1(x) means “f.

5.1 Composite Functions Goals 1.Form f(g(x)) = (f  g) (x) 2.Show that 2 Composites are Equal.

6-1: Operations on Functions (Composition of Functions)

How do we verify and find inverses of functions?

Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x f(x) = x + 4, g(x) = x

1.4 Building Functions from Functions

Review of 1.4 (Graphing) Compare the graph with.

Function Composition Given f(x) = 2x + 2 and g(x) = 2, find f ºg(x). f ºg(x)=f(g(x)Start on the inside. f(g(x)) g(x) = 2, so replace it. f(g(x)) = f(2)

FUNCTIONS REVIEW PRE-CALCULUS UNIT 1 REVIEW. STANDARD 1: DESCRIBE SUBSETS OF REAL NUMBERS What are the categories? Where would these be placed? 7, 6,

Finding Inverses (thru algebra) & Proving Inverses (thru composition) MM2A5b. Determine inverses of linear, quadratic, and power functions and functions.

Inverse Functions The inverse of a function is obtained by interchanging the x and y values of the original function. Inverse Function Notation: If the.

6.4 Notes – Use Inverse Functions. Inverse: Flips the domain and range values Reflects the graph in y = x line. Functions f and g are inverses of each.

5.3 Inverse Functions. Definition of Inverse Function A function of “g” is the inverse function of the function “f” if: f(g(x)) = x for each x in the.

Chapter 3: Transformations of Graphs and Data Lesson 8: Inverse Functions Mrs. Parziale.

7.4 Inverse Functions p. 422 What is an inverse relation? What do you switch to find an inverse relation? What notation is used for an inverse function?

Section 2.7 Combining Functions Objectives: To add, subtract, multiply and divide functions. Composition of functions.

Ch 9 – Properties and Attributes of Functions 9.5 – Functions and their Inverses.

Inverse Functions. Definition A function is a set of ordered pairs with no two first elements alike. f(x) = { (x,y) : (3, 2), (1, 4), (7, 6), (9,12) }

Function Operations and Composition MM2A5d. Use composition to verify that functions are inverses of each other.

Inverse Function Recap. Determine whether these functions are one-to-one. Problems 10 and 12 from red book.

5.3- Inverse Functions If for all values of x in the domains of f and g, then f and g are inverse functions.

Finding the Inverse of a Function Algebraically

Inverse Functions 5.3 Chapter 5 Functions 5.3.1

Warm-up: Given f(x) = 2x3 + 5 and g(x) = x2 – 3 Find (f ° g)(x)

Composition of Functions

Inverse Relations & Square Root Functions

Functions Review.

Section 5.1 Composite Functions.

Homework Questions.

= + 1 x x2 - 4 x x x2 x g(x) = f(x) = x2 - 4 g(f(x))

Please find your new assigned seat!

Warm up f(x) = x g(x) = 4 - x (f о g)(x)= (g о f)(x)=

Inverse Functions.

Activity 2.8 Study Time.

Functions and Their Inverses

Homework Questions.

Function Composition Section 8-7.

2-6: Combinations of Functions

2.6 Operations on Functions

Combinations of Functions

6.4 Use Inverse Functions.

3 Inverse Functions.

3.5 Operations on Functions

Warm Up Determine the domain of the function.

7.4 Inverse Functions p. 422.

Inverse Functions.

Function Composition Section 8-7.

Determine if 2 Functions are Inverses by Compositions

Function Composition.

Objective: to find and verify inverses of functions.

Warm Up Determine the domain of f(g(x)). f(x) = g(x) =

Section 2 – Composition of Functions

Warm-up: Given a line with slope -3 and a point on the line (2, 1) find three more points on the line. CW: Chapter 1 Review.

Review Slide Show.

Homework Questions.

Use Inverse Functions Notes 6.4.

Use Inverse Functions Notes 7.5 (Day 2).

Function Operations Function Composition

Replace inside with “x” of other function

7.4 Inverse Functions.

2-6: Combinations of Functions

FUNCTIONS & THEIR GRAPHS

Presentation transcript:

Objective: Find inverse functions. Warm up 1. a.Find (f o g)(x). b.Find the domain of f(g(x)).

2. a.Find f + g and its domain. a.Find f – g and its domain. a.Find and its domain.

3. Graph using transformations.

Example 1 Relation show number of students who got at least 90 on a quiz. (10, 90); (7, 90); (11, 90); (9, 90); (8, 90) a.Is the relation a function? b.Find the inverse. c.Is the inverse a function?

Example 2 Find the inverse. a. b.

c.

Quiz Tomorrow 1.6 Graphing using transformations:. Order of transformations.. Applying multiple transformations to functions such as: 1.7. Finding domain of functions (no graphs).. Finding composition of functions such as f(g(x)) or g(f(x)). Assignment Pg 272 #65, 67, 72, 75, 77, 88, 89, 90, 94, 96

Objective: Verify inverse functions. Warm up 1.Find the inverse function.

Inverse Functions Let f and g be two functions if f(g(x))=x and g(f(x))=x then f and g are inverse functions. Example 1 Verify and are inverse..

Example 2

Example 3 Verify and are inverse.

Assignment Pg 230 #35,36,45,46 Pg 240 #16, 18,24,25,26,27 Quiz Tomorrow on 1.6 and 1.7

f(x)= Fahrenheit, x=Celsius ; when x =30, then f(x)=86 g(x)=Celsius, x=Fahrenheit ; when x=86, then g(x)=?