Inverse Relations and Functions 7-7. Inverse Relations If a relation maps element a of its domain to element b of its range, the INVERSE RELATION “undoes”

Slides:

Advertisements

Similar presentations

One-to-one and Inverse Functions

Advertisements

Operations on Functions Composite Function:Combining a function within another function. Written as follows: Operations Notation: Sum: Difference: Product:

Inverse Functions Undoing What Functions Do. 6/1/2013 Inverse Functions 2 One-to-One Functions Definition A function f is a one-to-one function if no.

Section 1.8 Inverse Functions

What is a Relation? What is a Function? Have we seen these before??

Exponential/ Logarithmic

4-3 Relations Objective: Students will represent relations as sets of ordered pairs, tables, mappings, and graphs. Students will find the inverse of a.

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.

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

Section 1.8 Inverse Functions. The function f is a set of ordered pairs, (x,y), then the changes produced by f can be “undone” by reversing components.

Composite Functions Inverse Functions

Final Exam Review Pages 4-6  Inverses  Solving Radical Equations  Solving Radical Inequalities  Square Root (Domain/Range)

Relations and Functions

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

Functions Section 1.4. Relation The value of one variable is related to the value of a second variable A correspondence between two sets If x and y are.

Section 4.1 Inverse Functions. What are Inverse Operations? Inverse operations are operations that “undo” each other. Examples Addition and Subtraction.

6.4 Inverse Functions Part 1 Goal: Find inverses of linear functions.

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-1 Exponential and Logarithmic Functions Chapter 9.

Inverse functions: if f is one-to-one function with domain X and range Y and g is function with domain Y and range X then g is the inverse function of.

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

3.2 Inverse Functions. Functions A function maps each element in the domain to exactly 1 element in the range.

1.4 Functions and Inverses Move to page 1.2Grab and drag point P. What changes and what remains the same? Record some ordered pairs for point P and point.

Pre-Calc Chapter 1 section 7 The Inverse of a Function.

Holt Algebra Inverses of Relations and Functions Graph and recognize inverses of relations and functions. Find inverses of functions. Objectives.

Review Functions. Function A function is a special type of relation in which each element of the domain is paired with exactly one element of the range.

Inverse Relations and Functions

Objectives: 1)Students will be able to find the inverse of a function or relation. 2)Students will be able to determine whether two functions or relations.

7-8: Inverse Functions and Relations. Terms to Know Inverse relation: the set of ordered pairs obtained by reversing the coordinates of each original.

Section 2.7 Inverse Functions

Objectives: To find inverse functions graphically & algebraically.

New Functions from Old Section 1.3.

Relations and Functions

Inverse Functions Algebra III, Sec. 1.9 Objective

Watch this!! The Inverse Function Watch this!!

6.1 One-to-One Functions; Inverse Function

Chapter 6: Radical functions and rational exponents

6-7 Inverse Relations and Functions

Relations and Functions

Warmup Let f(x) = x – 3 and g(x) = x2. What is (f ○ g)(1)?

4-6 Formulizing Relations and Functions

Chapter 5: Inverse, Exponential, and Logarithmic Functions

One-to-One Functions and Inverse Functions

Inverse Functions 5.3 Chapter 5 Functions 5.3.1

Inverse Linear Functions

Inverse Functions.

Functions and Inverses

Functions Introduction.

4.1 Inverse Functions.

Section 2.7 Inverse Functions

Standards: MM2A5 – Students will explore inverses of functions.

4.1 One-to-One Functions; Inverse Function

Algebra 1 Section 5.2.

One-to-one and Inverse Functions

Relations and Functions

Section 1.8 Inverse Functions

6.1 One-to-One Functions; Inverse Function

Aim: What is the function notation?

Sec. 2.7 Inverse Functions.

Section 7.4 Inverse Functions

One-to-one and Inverse Functions

One-to-one and Inverse Functions

You can find and apply inverses to relations and functions

Section 4.1 Inverse Functions.

Exercise Give the domain and range of the following relation.

1.6 - Relations.

Composition of Inverses Calculator will be helpful!

Inverse Functions A function and its inverse function can be described as the "DO" and the "UNDO" functions. A function takes a starting value, performs.

Chapter 5: Exponential and Logarithmic Functions

• • • • • Check It Out! Example 1

3 Chapter Chapter 2 Graphing.

Presentation transcript:

Inverse Relations and Functions 7-7

Inverse Relations If a relation maps element a of its domain to element b of its range, the INVERSE RELATION “undoes” the relation and maps b back to a. So if (a,b) is an ordered pair of a relation, then (b,a) is an ordered pair of its inverse. If a relation maps element a of its domain to element b of its range, the INVERSE RELATION “undoes” the relation and maps b back to a. So if (a,b) is an ordered pair of a relation, then (b,a) is an ordered pair of its inverse RELATION r INVERSE OF RELATION r

Interchanging x and y Find the inverse of y = x 2 + 3

Functions and Relations Does define a function? Is its inverse a function?

Graphing a Relation and its Inverse The reflection over the line y = x is the graph of the inverse. You can also find points on the graph of the inverse by reversing the coordinates of the points on the relation.

Notation The inverse of f is denoted by f -1. Read f -1 as “the inverse of f” or as “f inverse.” The notation f(x) is used for functions, but f -1 (x) may be a relation that is not a function. If f and f -1, are functions, they are called inverse functions. For inverse functions and

Real Life Problems with Formulas Functions that model real-life situations are frequently expressed as formulas with letters that remind you of the variables they represent. When finding the inverse of a formula, it would be very confusing to interchange the letters. Keep the letters the same and just solve the formula for the other variable