10th Edition

ISBN: 9780134781945

Author: Demana

Publisher: PEARSON

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Textbook Question

Chapter 1.4, Problem 2E

In Exercises 1−4 find formulas for the functions $f + g , f − g$ , and $f g$ . Give the domain of each.

2. $f x = x − 1 2 ; g x = 3 − x$

Expert Solution & Answer

Solution

To find: The formula and domain for functions $f+g$ $f+g$ .

The required functions are: $f+g=x2−3x+4$ and $f−g=x2−x−2$ . The domain of each function $f+g$ and $f−g$ is set of real numbers $−∞,∞ or ℝ$ .

Given data: The functions $fx$ and $gx$ are $fx=x−12$ and $gx=3−x$ .

Method/Formula used:

The sum and difference of the two functions $fx$ and $gx$ is also a function given by $fx+gx=f+gx$ , and $fx−gx=f−gx$ . The domain of resulting function $f+gx$ and $f−gx$ are the values of values of x that define $f+gx$ and $f−gx$ .

Calculation:

The given functions are $fx=x−12$ ; $gx=3−x$ . Therefore, using the definition of $fx+gx$ and $fx−gx$ are:

$f+gx=fx+gx=x−12+3−x=x2−2x+1+3−x=x2−3x+4$

Since, $x2−3x+4$ is a polynomial function (algebraic expression), defined for all real numbers. Therefore, the domain of $f+gx$ is $−∞,∞ or ℝ$ .

$f−gx=fx−gx=x−12−3−x=x2−2x+1−3+x=x2−x−2$

Since, $x2−x−2$ is a polynomial (algebraic expression), defined for all real numbers. Therefore, the domain of $f−gx$ is $−∞,∞ or ℝ$ .

Chapter 1.4, Problem 1E

Chapter 1.4, Problem 3E

Chapter 1 Solutions

PRECALCULUS:GRAPHICAL,...-W/ACCESS

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

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Prob. 7QR Ch. 1.4 - Prob. 8QR Ch. 1.4 - Prob. 9QR Ch. 1.4 - Prob. 10QR Ch. 1.4 - In Exercises 14 find formulas for the functions...Ch. 1.4 - In Exercises 14 find formulas for the functions...Ch. 1.4 - Prob. 3E Ch. 1.4 - Prob. 4E Ch. 1.4 - Prob. 5E Ch. 1.4 - Prob. 6E Ch. 1.4 - Prob. 7E Ch. 1.4 - Prob. 8E Ch. 1.4 - Prob. 9E Ch. 1.4 - Prob. 10E Ch. 1.4 - Prob. 11E Ch. 1.4 - Prob. 12E Ch. 1.4 - Prob. 13E Ch. 1.4 - Prob. 14E Ch. 1.4 - Prob. 15E Ch. 1.4 - Prob. 16E Ch. 1.4 - Prob. 17E Ch. 1.4 - Prob. 18E Ch. 1.4 - Prob. 19E Ch. 1.4 - Prob. 20E Ch. 1.4 - Prob. 21E Ch. 1.4 - Prob. 22E Ch. 1.4 - Prob. 23E Ch. 1.4 - Prob. 24E Ch. 1.4 - Prob. 25E Ch. 1.4 - Prob. 26E Ch. 1.4 - Prob. 27E Ch. 1.4 - Prob. 28E Ch. 1.4 - Prob. 29E Ch. 1.4 - Prob. 30E Ch. 1.4 - Prob. 31E Ch. 1.4 - Prob. 32E Ch. 1.4 - Prob. 33E Ch. 1.4 - Prob. 34E Ch. 1.4 - Prob. 35E Ch. 1.4 - Prob. 36E Ch. 1.4 - Prob. 37E Ch. 1.4 - Prob. 38E Ch. 1.4 - Prob. 39E Ch. 1.4 - Prob. 40E Ch. 1.4 - Prob. 41E Ch. 1.4 - Prob. 42E Ch. 1.4 - Prob. 43E Ch. 1.4 - 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In Exercises 1−4 find formulas for the functions f + g , f − g , and f g . Give the domain of each. 2. f x = x − 1 2 ; g x = 3 − x

Solution Summary: The author explains the formula and domain of the functions f+g and g(x).

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Chapter 1 Solutions