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

Slides:

Advertisements

Similar presentations

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

Advertisements

6.2 One-to-One Functions; 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

2.1 Functions and their Graphs p. 67. Assignment Pp #5-48 all.

Algebra 2: Section 7.4 Inverse Functions.

nth Roots and Rational Exponents

5.2 Inverse Function 2/22/2013.

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

N th Roots and Rational Exponents What you should learn: Evaluate nth roots of real numbers using both radical notation and rational exponent notation.

INVERSE FUNCTIONS Section 3.3. Set X Set Y Remember we talked about functions--- taking a set X and mapping into a Set Y An inverse.

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.

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

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.

2.1 Functions and their Graphs page 67. Learning Targets I can determine whether a given relations is a function. I can represent relations and function.

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.

Objectives 1. To determine if a relation is a function.

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

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

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.

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?

7.8 Inverse Functions and Relations Horizontal line Test.

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

Chapter 3: Functions and Graphs 3.6: Inverse Functions Essential Question: How do we algebraically determine the inverse of a function.

Function A FUNCTION is a mathematical “rule” that for each “input” (x-value) there is one and only one “output” (y – value). Set of Ordered Pairs: (input,

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

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

Function A FUNCTION is a mathematical “rule” that for each “input” (x-value) there is one and only one “output” (y – value). Set of Ordered Pairs: (input,

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) }

Objectives: To find inverse functions graphically & algebraically.

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

Ch. 1 – Functions and Their Graphs

DO NOW: Perform the indicated operation.

INVERSE FUNCTIONS.

Inverse Functions 5.3 Chapter 5 Functions 5.3.1

INVERSE FUNCTIONS.

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

Inverse Relations and Functions

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

INVERSE FUNCTIONS.

Inverse Functions.

Finding Inverse Functions (2.7.1)

Activity 2.8 Study Time.

1.9 Inverse Functions f-1(x) Inverse functions have symmetry

5.6 Inverse Functions.

Composition of Functions And Inverse Functions.

4-5 Inverse Functions.

Warm-Up For the following, make a T-Chart and sketch a graph for x ={-2, -1, 0, 1, 2}

6.4 Use Inverse Functions.

3 Inverse Functions.

Sec. 2.7 Inverse Functions.

Write in scientific notation.

Inverse Functions Inverse Functions.

7.4 Inverse Functions p. 422.

Objective: to find and verify inverses of functions.

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

1.6 Inverse Functions.

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

7.4 Inverse Functions.

1.6 Inverse Functions.

Graph the function and it’s inverse On the same graph f(x) = 2x + 10

Presentation transcript:

6.7 Notes – Inverse Functions

Notice how the x-y values are reversed for the original function and the reflected functions.

Review from chapter 2 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 Equation Table of values Graph

Inverse relation – just think: switch the x & y-values. x = y 2 x y ** the inverse of an equation: switch the x & y and solve for y. ** the inverse of a table: switch the x & y. ** the inverse of a graph: the reflection of the original graph in the line y = x.

Ex: Find an inverse of y = -3x+6. Steps: -switch x & y -solve for y y = -3x+6 x = -3y+6 x-6 = -3y

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 inverse of x”

Meaning find f(g(x)) and g(f(x)). If they both equal x, then they are inverses. ** Because f(g(x))=x and g(f(x))=x, they are inverses.

To find the inverse of a function:

Ex: (a)Find the inverse of f(x)=x 5. 1.y = x 5 2.x = y 5 3. (b) Is f -1 (x) a function? (hint: look at the graph! Does it pass the vertical line test?) Yes, f -1 (x) is a function.

Horizontal Line Test Used to determine whether a function’s inverse will be a function by seeing if the original function passes the h hh horizontal line test. If the original function p pp passes the horizontal line test, then its i ii inverse is a function. If the original function d dd does not pass the horizontal line test, then its i ii inverse is not a function.

Ex: Graph the function f(x)=x 2 and determine whether its inverse is a function. Graph does not pass the horizontal line test, therefore the inverse is not a function.

Ex: f(x)=2x 2 -4 Determine whether f -1 (x) is a function, then find the inverse equation. f -1 (x)= is not a function. y = 2x 2 -4 x = 2y 2 -4 x+4 = 2y 2 OR, if you fix the tent in the basement…

Ex: g(x)=2x 3 Inverse is a function! y=2x 3 x=2y 3 OR, if you fix the tent in the basement…