Algebra 2: Section 7.4 Inverse Functions.

Slides:

Advertisements

Similar presentations

One-to-One and Inverse Functions Section 3.5. Function and One-to-One  Function- each value of x corresponds to only one y – value Use vertical line.

Advertisements

1.6 Inverse Functions Students will find inverse functions informally and verify that two functions are inverse functions of each other. Students will.

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

6.2 One-to-One Functions; Inverse Functions

1.4c Inverse Relations and Inverse 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.

Precalculus 1.7 INVERSE FUNCTIONS.

Functions and Their Inverses

INVERSE FUNCTIONS.  Prove that and are inverses of each other  Complete warm up individually and then compare to a neighbor END IN MIND.

Warm-up 3.3 Let and perform the indicated operation

Objectives Determine whether the inverse of a function is a function.

Inverses Algebraically 2 Objectives I can find the inverse of a relation algebraically.

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,

Section 2.8 One-to-One Functions and Their Inverses.

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

Parametric and Inverse Functions Nate Hutnik Aidan Lindvig Craig Freeh.

Combinations of Functions & Inverse Functions Obj: Be able to work with combinations/compositions of functions. Be able to find inverse functions. TS:

DO NOW: 6.3: w/s C: Perform the indicated operation. 1.) Find g(f(x)) if f(x) = 2x 2 – x and g(x) = 2.) Find g(h(8)) if g(x) = -x 2 and h(x) =

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.

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

INVERSE FUNCTIONS. Set X Set Y Remember we talked about functions--- taking a set X and mapping into a Set Y An inverse function.

CHAPTER 6 SECTION 6 : FUNCTIONS AND THEIR INVERSES.

3.4 Use Inverse Functions p. 190 What is an inverse relation?

Inverse Functions Section 7.4.

How do we verify and find inverses of functions?

Inverse Functions.

Lesson 1.6 Inverse Functions. Inverse Function, f -1 (x): Domain consists of the range of the original function Range consists of the domain of the original.

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

Pg. 136 Homework Pg. 136#18 – 28 even, 33, 34 Pg. 140 #102 – 107 #13f(g(x) = g(f(x) = x#14f(g(x) = g(f(x) = x #15f(g(x) = g(f(x) = x #17No, it fails the.

1.4 Building Functions from Functions

One-to-one and Inverse Functions. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Review: A is any set of ordered pairs. A function.

Review Relation – a mapping of input values (x-values) onto output values (y-values). Here are 3 ways to show the same relation. y = x 2 x y

Relations are a pairing of input and output values. You could say a list of points.

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

Section 8.7 Inverse Functions. What is a Function? domain range Relationship between inputs (domain) and outputs (range) such that each input produces.

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?

Advanced Algebra Notes Section 6.4: Use Inverse Functions In Chapter 2 we learned that a ___________ is a set of ordered pairs where the domains are mapped.

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) }

5.3 Inverse Functions (Part I). Objectives Verify that one function is the inverse function of another function. Determine whether a function has an inverse.

1.6 Inverse Functions. Objectives Find inverse functions informally and verify that two functions are inverse functions of each other. Determine from.

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

One-to-one and Inverse Functions

Objectives: To find inverse functions graphically & algebraically.

Warm Up Solve for x in terms of y

New Functions from Old Section 1.3.

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

DO NOW: Perform the indicated operation.

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

Functions Review.

Inverse Relations and Functions

Section 1.5 Inverse Functions

Inverse Functions.

Inverse Functions.

Inverse Inverse.

One-to-one and Inverse Functions

Composition of Functions And Inverse Functions.

6.4 Use Inverse Functions.

3 Inverse Functions.

One-to-one and Inverse Functions

One-to-one and Inverse Functions

7.4 Inverse Functions p. 422.

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.

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.

7.4 Inverse Functions.

Do Now: Given f(x) = 2x + 8 and g(x) = 3x2 – 1 find the following.

Presentation transcript:

Algebra 2: Section 7.4 Inverse Functions

Inverse Relation Maps the output back to original input Domain of inverse is the range of the original function

Finding Inverse of a Function (Algebraically) Rewrite function name; usually f(x) as y Switch the x’s and y’s Solve for y

Finding Inverse of a Function

Power Function A function of the form Where a is a real number b is rational

Finding Inverse of a Function

Finding Inverse of a Function

Verifying Functions are Inverses Functions are inverses of each other if… f(g(x)) = x AND g(f(x)) = x f -1(x) = g(x) Reads “inverse of f”

Verify that f and g are inverses f and g are inverses of each other!!!

Homework P.426 #16-24 all #25-31 odd

Inverse Functions (Day 2) Algebra 2: Section 7.4 Inverse Functions (Day 2)

Warm-Up What is the range of a function? Output values y-values What is the domain of a function? Input values x-values

Finding Inverses of a Function (Graphically) To create the inverse graph of a function… Reflect the original graph across the line y = x. Examples on Board!!! Swap x and y values of plotted points y = x2 y = x3 Sketchpad Example

Warm-Up Write the image of each point after its reflection in the line y = x. (2, 3)  (-2, 4)  (-1, -1)  (1, -3) 

Inverse Functions An inverse relation may or may not be a function (even if the original IS a function!) Graph original in calculator (y1) Graph inverse in calculator (y2) Is the inverse a function? How could you tell by looking at only the graph of the original function?

Horizontal Line Test Look at original function If no horizontal line intersects the graph of the function more than once, then the inverse of the original will also be a function So, if a relation passes the vertical and horizontal line tests then the original relation and its inverse are functions Vertical Line Test  original function Horizontal Line Test  inverse function

Examples: Find the inverse

Homework P.427 #36-56 all Use graphing calculator for #48-56 Draw sketch of graph on homework

Verifying if Functions are Inverses Using TI-83 Enter each function into Y1 and Y2 Enter Y1(Y2) into Y3 Enter Y2(Y1) into Y4 Turn on graph of Y3 only See if it is the graph of y=x Turn on graph of Y4 only Verify #31, p.426 using TI-83