Pre-Calculus - Section 4.5 INVERSE FUNCTIONS. WARM-UP.

Slides:

Advertisements

Similar presentations

The Domain of f is the set of all allowable inputs (x values)

Advertisements

Composition of Functions

6.2 One-to-One Functions; Inverse Functions

Rational Exponents and Radical Functions

Example 1A: Using the Horizontal-Line Test

Precalculus 1.7 INVERSE FUNCTIONS.

Inverse Functions and their Representations Lesson 5.2.

Inverse Functions Consider the function f illustrated by the mapping diagram. The function f takes the domain values of 1, 8 and 64 and produces the corresponding.

Algebra 2: Section 7.4 Inverse Functions.

Warm-up 3.3 Let and perform the indicated operation

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.

Composite Functions Inverse Functions

1. Section 2.4 Composition and Inverse Functions 2.

1 PRECALCULUS I Dr. Claude S. Moore Danville Community College Composite and Inverse Functions Translation, combination, composite Inverse, vertical/horizontal.

Math-3 Lesson 4-1 Inverse Functions. Definition A function is a set of ordered pairs with no two first elements alike. – f(x) = { (x,y) : (3, 2), (1,

Chapter 1 Functions & Graphs Mr. J. Focht PreCalculus OHHS.

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

Advanced Algebra with Trigonometry

1.4 FUNCTIONS!!! CALCULUS 9/10/14 -9/11/14. WARM-UP  Write a general equation to represent the total cost, C, in a business problem. How is it different.

Algebra II 7-4 Notes. Inverses  In section 2-1 we learned that a relation is a mapping of input values onto output values. An _______ __________ maps.

FUNCTION NOTATION AND EVALUATING FUNCTIONS SECTIONS 5.1 & 14.1B.

Goal: Find and use inverses of linear and nonlinear functions.

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.

Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.

CHAPTER 6 SECTION 6 : FUNCTIONS AND THEIR INVERSES.

Warmup Alg 31 Jan Agenda Don't forget about resources on mrwaddell.net Section 6.4: Inverses of functions Using “Composition” to prove inverse Find.

Inverse Functions Section 7.4.

How do we verify and find inverses of functions?

Do Now Find the domain & range:. Answers to Homework

7.8 Inverse Functions and Relations Horizontal line Test.

6.4 Inverse Functions Part 1 Goal: Find inverses of linear 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

7.5 Inverses of Functions 7.5 Inverses of Functions Objectives: Find the inverse of a relation or function Determine whether the inverse of a function.

Temperature Readings The equation to convert the temperature from degrees Fahrenheit to degrees Celsius is: c(x) = (x - 32) The equation to convert the.

Warm-Up . Homework Questions Domain Algebraically Pre-Calculus Mrs. Ramsey.

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

One-to-one and Inverse Functions 2015/16 Digital Lesson.

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.

1.8 Inverse Functions. Any function can be represented by a set of ordered pairs. For example: f(x) = x + 5 → goes from the set A = {1, 2, 3, 4} to the.

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

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

Ch. 7 Day 6 Book Section 7.6 Function Operations.

Quiz f(x) = 2x + 3 and f(g(x)) = ? (f + g)(x) = ? 3. What is the domain? 3 f(x) - 2 g(x) = ? 4.

Operations with Functions

3.5 Operations on Functions

Objectives: To find inverse functions graphically & algebraically.

Warm Up Solve for x in terms of y

Suppose that and find and

Functions Review.

Homework Questions.

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

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

Activity 2.8 Study Time.

x g(x) yof g f(x) yof f input output input output

Functions and Their Inverses

Homework Questions.

Composition of Functions And Inverse Functions.

6.4 Use Inverse Functions.

Sec. 2.7 Inverse Functions.

6.4 - Use Inverse Functions

Warm Up Determine the domain of the function.

Section 4.1 Inverse Functions.

Page 196 1) 3) 5) 7) 9) 11) 13) g(f(3)) = -25, f(g(1)) = 1, f(f(0)) = 4 15) 1 17) 30 19) f(g(x)) = (x + 3)2 g(f(x)) = x2 + 3 Domain: All Reals 21) 5/15/2019.

Determine if 2 Functions are Inverses by Compositions

Objective: to find and verify inverses of functions.

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

Section 4.1: Inverses If the functions f and g satisfy two conditions:

Use Inverse Functions Notes 6.4.

Use Inverse Functions Notes 7.5 (Day 2).

Algebra 2 Ch.7 Notes Page 52 P Function Operations.

Presentation transcript:

Pre-Calculus - Section 4.5 INVERSE FUNCTIONS

WARM-UP

 When is f a function?  When each input goes to exactly 1 output  Determine if the following are functions REVIEW: FUNCTIONS xy xy

 Inverse functions “undo” each other. WHAT IS AN INVERSE REALLY? DomainRange Function RangeDomain Inverse

WE USES THE CONCEPT OF INVERSE FUNCTIONS ALL OF THE TIME. For example, someone give us directions to their house. Turn right, go three blocks, turn left, go one block, and turn left again. We would use the inverse to go home. Come up with another example of inverse functions in every day life.

HOW TO FIND AN INVERSE GIVEN POINTS x f(x) xf -1 (x)

EXAMPLE 1

 Horizontal Line Test:  If one output from the original function goes to multiple inputs, then what will happen when with the inverse?  Determine if the inverse will be a function: WHEN IS THE INVERSE A FUNCTION?

HOW TO CREATE AN INVERSE

EXAMPLE 2

YOU TRY. Find the inverse function:

EXAMPLE 3

 Functions f and g are inverse if g(f(x)) = x and f(g(x)) = x for all x in either domain. COMPOSITION

EXAMPLE 3

 Textbook: p.149 #7-15, 20 ***rule = equation of the inverse HOMEWORK