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I need the following problem solved with step by step explanations.

An example has been provided by the instructor. I can put the paper in APA format and write the opening and closing paragraphs.


Composition and Inverse

Read the following instructions to complete this assignment:
1. We define the following functions:

f (x) = 2x +5 g (x) = x² -3 h (x) = 7-x
3
o Compute (f – h) (4)
o Evaluate the following two compositions:
A: ( f ºg)(x)

B: (h ºg)(x)
o Graph the g(x) function and transform it so that the graph is moved 6 units to the right and 7 units down.
o Find the inverse functions:
C: f ¯¹(x)

D: h¯¹(x)
2. Write a two- to three-page paper (not including the title page) 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, do the following:
• Demonstrate your solution to the above problems, making sure to include all mathematical work as well as explanations for each step.

Running head: COMPOSITION AND INVERSE 1 Running header should use a shortened version of the title if the title is long. Page number is located at right margin. (full title; centered horizontally & vertically) Composition and Inverse John Q. Student MAT 222 Week 1 Assignment Instructor’s Name Date
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COMPOSITION AND INVERSE 2 Composition and Inverse (title required on first line) Functions provide an opportunity for manipulating expressions using different values. These values can help business owners, data analysts, and even the consumer compare rates and data. Functions also extend independent (x) and dependent (y) variables by graphing in the coordinate plane and creating a visual demonstration of the relationship. The following functions will be used in the required problems. f(x) = 5 x – 3 g(x) = x 2 + 2 h(x ) = 3 + x 7 The first task is to compute ( f – h )(4). ( f – h )(4) = f (4) – h (4) Because of rules of composition, each function may be calculated separately and then subtracted. f (4) = 5(4) – 3 The x was replaced with the 4 from the problem. f (4) = 20 – 3 Order of operations was used to evaluate the function. f (4) = 17 h (4) = (3 + 4)/7 The same process is used for h (4) and f (4). h (4) = 7/7 h (4) = 1 ( f – h )(4) = 17 – 1 ( f – h )(4) = 16 This is the solution after substituting the values and subtracting. Next, two pairs of the functions will be composed into each other. One option to find the solution for the function, g ( x ),will be to calculate it and then substitute for the x value in the f( x ). The option used here is to replace the x in the f function with the g function. This means the rule of f will work on g . This means the rule of f will work on the problem: ( f ° g )( x ) = f ( g ( x )).
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Subject: College Algebra, Math

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