Composition 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 6 units to the right and 7 units down. Find the inverse functions and .
1. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include: * Your solutions to the above problems, making sure to include all mathematical work for both problems, as well as explaining each step. * A discussion of the applicability of functions to the real world, based upon your reading of Chapter 11 of Elementary and Intermediate Algebra. Be sure to use specific examples, a brief discussion of why your examples are important, and to cite your sources. The paper must be at least two pages in length and formatted according to APA style. Cite your resources in text and on the reference page. For information regarding APA samples and tutorials, visit the Ashford Writing Center, within the Learning Resources tab on the left navigation toolbar.

INSTRUCTOR GUIDANCE EXAMPLE: Week Five Assignment
Composition and Inverse
We are working with the following functions:
f(x) = 5x – 3 g(x) = x2 + 2 h(x) = 3 + x
7
We have been asked to compute (f – h)(4).
(f – h)(4) = f(4) – h(4) So we can evaluation each separately and then subtract.
f(4) = 5(4) – 3
= 20 – 3 = 17 f(4) = 17
h(4) = (3 + 4)/7
= 7/7 = 1 h(4) = 1
(f – h)(4) = 17 – 1 = 16 This is our answer.
Next we are to compose two pairs of the functions into each other. First we will...

...
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 following functions to solve the problem.
f(x)+2x+5 g(x)=x^2-3 h(x)=7-x
______
3
The first step is to compute the required problem (f-h)(4).
(f-h)(4)
f(4)-h(4) The first step is to multiply 4 into f and h to be subtracted from each other. Since the equation require functions f and h, we will plug them into the problem.
f(4)-h(4)= [2(4)+5]-[7-(4)]
_____
[3] Solve for functions f and h while substituting the x for the number 4
=13 - 11
___
3 Subtract
= 28
___
3 Final answer
The next step is to evaluate the following compositions.
A: (f o g)(x)= 2(x^2-3)+5 Multiply 2 to the equation in the parenthesis
= 2x^2-6+5 Sutract -6 from 5
= 2x^2-1...

...Composition and Inverse
Mat222
2/23/2013
This week we have been assigned three functions which we must evaluate. These are the functions which we have to evaluate this week.
fx=2x+3 gx=x2-3 hx=7-x3
We have been asked to compute(f-h)(4).
So we can evaluate each separately and then subtract.
f-h4=f4-h(4)
f4=24+3
=8+3=11 f4=11
h4=7-43
=33=1 h4=1
This is our final answer.
f-h4=11-1=10
Next we are to compare two pairs of the functions into each other. First we will work out.
f°gx=f(gx) This means the rule of f will work on g.
=fx2-3 Here f is now going to work on the rule of g.
=2x2-3+5 The rule of f is applied to g.
=2x2-6+5 Simplifying
f°gx=2x2-1 The final results.
Now we will compose the following:
h°gx=h(gx) The rule of h will work on g.
=hx2-3
=-7+(x2-3)3 The rule of h is applied to g.
h°gx=-10+x23 The final results.
Next we are asked to transform g(x) so that the graph is placed 6 units to the right and 7 units downward for where it would be right now.
* Six units to the right means to put a -6 in with x to be squared.
* Seven units downward means to put -7 outside of the squaring.
* The new functions will look like this:
gx=(x-6)2-3-7
gx=(x-6)2-10
Our last job is to find the inverse of two of our functions, f and h. To find the...

...
Composition and Inverse
Alicia Frambro
MAT 222: Intermediate Algebra
Prof: Michael Smith
September 22, 2013
Composition and Inverse
When using functions, there are different ways to solve various values. Many companies use these functions to monitor business pertaining gross profit and many other operations such as adjusting productivity. Visual examples of these functions are graphs. They provide a visual relationship between composition and inverse solutions as well and the difference between profit gain and profit loss for a business.
The following functions will be used to solve certain problems.
𝘩(x) =
Use rule of composition and solve which is f(4)-h(4).
f(x)-h(x)= 2x+5-(7-x)
2(4) +5- Substitute 4 for x.
8+ 5- Use order of operations to solve.
8+5-1= 12 Therefore (f-h)(4)= 12
Evaluate two compositions of the above functions.
A. (fog)(x)
B. (fog)(x)
The method that should be used to solve is to find the solution of one function and then substitute the solution for x in the other solution. For A we would first solve for g(x) and substitute the solution for x into f(x).
A. (fog)(x)= f(g(x))
(fog)(x)= f(x2-3)
(fog)(x)= 2(x2-3) +5 Substitute g(x) for x in f(x).
(fog)(x) = 2x2-6+5 Simplify by using the distributive property and order of
operations.
(fog)(x)= 2x2 -1 Answer.
B....

...
COMPOSITION AND INVERSE FUNCTIONS
Composition and Inverse Functions
Kimberly Harris
MAT 222 Week 5 Assignment
Instructor: Donna Wall
July 18, 2014
Composition and Inverse Functions
In this week’s assignment I am given three Composition and Inverse Functions. Functions gives an opportunity for manipulating experiences using different values. What these values does is to help business owners and others the opportunity to compare rates and dates. Functions can extend independent (x) and dependent (y) variables by graphing the coordinate plane and to create a visual demonstration of the relationship.
The three functions that will be used in the following problems are as follows:
f(x) = 2x = 5 g(x)= x² – 3 h(x) = 2 – x
3
The first thing I have to do is to compute (f – h)(4).
(f – h)(4) = f(4) – h(4) Because of the rules of composition, each function can be calculated separately and then subtracted.
f(4) = 2(4) = 5 The x was...

...Composition and Inverse
MAT222
Composition and Inverse
The following functions will be used in this week’s assignment.
1. fx=2x+5
2. gx=x2-3
3. hx=7-x3
We are first asked to compute f-h4. Like many algebra problems, the solution becomes obvious, or at least easier, once it has been rewritten into a different format. We will solve the problem in this way:
f-h(4) - Original expression
f4-h4 - Rewritten
24+5-7-43 - Substitute 4 for x
8+5- 33 - Simplify
13-1 - Simplify further
12 -Solution
The second problem involves composing two pairs into each other.
f°g(x) - Original expression
f(gx) - Rewritten so that rule of f will apply
fx2-3 - g inserted
2x2-3+5 - f applied to g
2x2-6+5 - Simplified
2x2-1 - Solution
The third problem also involves composing two pairs into each other.
h°g(x) - Original expression
h(g(x)) - Rewritten so that rule of h will apply to g
hx2-3 - g inserted
7-(x2-3)3 - h applied to g
21-3(x2-3) - Multiply numerator and denominator by 3
21-3x2-9 - Simplified
12-3x2 - Simplified
-3x2+12 - Rewritten
x2+4 - Solution
The fourth problem involves transforming the function gx=(x2-3) so that it appears on a different x and y axis. In order to transform the g(x) function six points to the right and seven down, we must modify the equation in the following way:
gx=(x2-3)...

...Rough Notes :: By the Rambling Librarian (Singapore)
An online jotter book for books and other stuff he’s read
Home
About this blog
Ideas for SciFi Reading Group
The DDC
Corak: patterns and proverbs of nature/ Omar Ariff & Noraini Jane Books/ Magazines read in 2008
An autobiography or the story of my experiments with truth/ Mohandas K. Gandhi
December 31, 2008
Ivan Chew Biography (DDC 920), Books, Non-Fiction 1 Comment
cover
(Translated from the original in Gujarati)
Other title: Satyanā prayogo athavā ātmakathā
NLB Call No.: 954.035 GAN
This book is about his pursuit towards self- realisation. It’s not an autobiography and some parts of the book, Gandhi presumes you know the context.
It’s a must-read to know more about the man, rather than the myth.
BOOK HIGHLIGHTS
Index pages 458 – 461 is an excellent summary of key points in his life, as described in the book.
Gandhi clarifies it is a book documenting his observations of his seeking various Truths. His Life’s Experiments.
In his Introduction, he explains why he agreed to write the book.
p X. “If anything that I write in these pages should touch the reader as touched with pride, then he must take it that there is something wrong with my quest, and that my glimpse are nothing more than,mirage. Let hundreds like me perish, but let the truth prevail. Let us not reduce the standard of truth for even by a hair’s breath from judging erring mere mortals like myself.”
“I hope and pray...

...Kelsey Fiely
Composition 1
Cause/Effect
November 12, 2014
Single Parent Families
Single parenting has several effects on both the children and the parent. These can include the risk, from the quality of parenting to the exposure of stress; the advantages, from the confidence of both the child and parent to the strong bond they have with each other; and the disadvantages, from the poor financial status to the effects that take place for both the child and the parent. These choices that parents make could potentially change their children’s lives. There are many risks involved in single parenting that affect that children.
Risk is a factor that comes with being a single parent. Economic hardship is a large part of single parenting. The children are often at an economic disadvantage. When single parenting, the parent only has one income, so they are automatically at a disadvantage than a family with two stable incomes (Amato). Children are six times more likely to be deprived in a one parent family (White 10). Only two percent of children in two-parent families will experience poverty during childhood for seven years or more, compared to twenty-two percent of children in one-parent families (White 11). Children that experience one-parent families are often more likely to get pregnant at a young age, not finish high school, deal with drug abuse, and get in trouble with the law (White 11).
Children’s emotional and social well-being is a predictor of the quality...

...5.1 Inverse Functions
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...

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