One-to-One Functions
* One-to-one function is where each x-value corresponds to one y-value, and each y-value corresponds to only one x-value *
* Horizontal line test – a function is one-to-one if every horizontal line intersects the graph of the function at most once * Examples: Determine whether the following functions are one-to-one

* In general, a function that is either increasing or decreasing on its entire domain, such as must be one-to-one * Tests to Determine Whether a Function is One-to-One
* Show that f(a) = f(b) implies a = b; then the function is one-to-one * Every y-value corresponds to no more than one x-value; to show that the function is not one-to-one, find at least two x-values that produce the same y-value * Use the horizontal line test

* If the function either increases or decreases on its entire domain, then it is one-to-one

Inverse Functions
* Let be a one-to-one function. Then g is the inverse function of if: *
* Examples: Determine whether f and g are inverses *
*
*
* Inverse of a function is denoted as
* By definition of inverse function, the domain of f is the range of and the range of f is the domain of. * To find the inverse of a one-to-one function, interchange the x- and y-values of each of its ordered pairs. * Functions that are not one-to-one do not have an inverse

* Examples: If the functions are one-to-one, find their inverses. *

* Steps for Finding the Equation of the Inverse of a Function * Interchange x and y
* Solve for y
* Replace y with
* Examples: For each function that is one-to-one, a) write an equation for the inverse function in the form , b) graph the function & its inverse, c) give the domain and range of the function...

...and Inverse
Jack Lewis
Mat 222
Instructor: Dr. Dariush Azimi
January 14, 2013
Composition and Inverse
The assignment paper for this week is to define the following functions of Elementary and Intermediate Algebra: Problem number 1) fx=2x+5, Problem number 2) gx=x2- 3, and Problem number 3) hx= 7-x3.
Compute (f – h)(4).
Evaluate the following two compositions: and .
Transform the g(x) function so that the graph is moved...

...COMPOSITION AND INVERSEFUNCTIONS
Composition and InverseFunctions
Kimberly Harris
MAT 222 Week 5 Assignment
Instructor: Donna Wall
July 18, 2014
Composition and InverseFunctions
In this week’s assignment I am given three Composition and InverseFunctions. Functions gives an opportunity for manipulating experiences using different...

...
Composition and Inverse
Student Name
MATH 222 Week 5 Assignment
Instructor Name
Date
Composition and Inverse
This week assignment was to understand and solve for composition and inversion. With the given problems and functions I will demonstrate how to compute a problem using composition. Then finally I will demonstrate how to solve a function using inversion.
I will define the...

...which relation is a function? State your reason.
Part 2
a) You are required to come out with an attractive and creative card. Your card must have the following information.
i) a family photo
ii) a family tree
b) Write a short description about your family in not more than 150 words.
Part 3
Based on Diagram 3, answer the following questions.
Diagram 3
Find
a) function [pic] and...

...:…………………………………………..
Date received
……………………………………..
Date completed …………………………. Marks of the Topical Test : ……………………………..
Prepared by : PN HJH SARIPAH AHMAD Sekolah Menengah Sains Muzaffar Syah Melaka 75450 AYER KEROH MELAKA
1
LEARNING AREA : FUNCTIONS Learning Objectives : Understand the concept of relations Learning Outcomes : Student will be able to
1.1 Represent relation using a) arrow diagram , b) ordered pairs, c)graphs 1.2 Identify domain, co domain,...

...CIRCULAR FUNCTIONS
A different name of an angle is circular functions. Communicate the direction of a triangle to the length of the surface of a triangle. Trigonometric functions are important of triangles and form episodic occurrence, along with many complementary applications. Trigonometric functions have a wide range of uses including calculating indefinite lengths along with angles in triangles.
Trigonometric functions...

...
Composition and Inverse
Cindy Dean
Intermediate Algebra: MAT 222
Instructor:
February 14, 2014
Composition and Inverse
In this week’s assignment, I will be solving functions with different values and variables. Many companies and businesses, use these methods to either make progress or to change something that will benefit their success. The first function is:
(f – h)(4)
f(4) – h(4) I...