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

The required functions are: $f+g=x+x+3$ , $f−g=x−x+3$ and $f.g=x⋅x+3$ . The domain of each function $f+g$ , $f−g$ and $fg$ is the set of real numbers $x∈0,∞$ .

Given data: The functions $fx$ and $gx$ are $fx=x$ ; $gx=x+3$ .

Method/Formula used:

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

Calculation:

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

$f+gx$ :

$f+gx=fx+gx=x+x+3$

The function $f+g=x+x+3$ is not defined when $x<0$ .Therefore, the domain of $f+gx$ is $0,∞$ .

$f-gx$ :

$f−gx=fx−gx==x−x+3$

The function $f−g=x−x+3$ is not defined when $x<0$ .Therefore, the domain of $f+gx$ is $0,∞$ .

$fgx$ :

$fgx=xx+3$

The function $f.g=x⋅x+3$ is not defined when $x<0$ .Therefore, the domain of $fgx$ is $0,∞$ .

The graphs of functions $x+x+3$ , $x−x+3$ , and $x⋅x+3$ are shown in Fig. (1), here that also shows that the functions $x+x+3$ , $x−x+3$ , and $x⋅x+3$ defined for all $x≥0$ , asserting that the domain of each of these function is $0,∞$ .

Chapter 1.4, Problem 3E

Chapter 1.4, Problem 5E

Chapter 1 Solutions

PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)

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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Give...Ch. 1.5 - Prob. 15E Ch. 1.5 - Prob. 16E Ch. 1.5 - Prob. 17E Ch. 1.5 - Prob. 18E Ch. 1.5 - Prob. 19E Ch. 1.5 - Prob. 20E Ch. 1.5 - Prob. 21E Ch. 1.5 - Prob. 22E Ch. 1.5 - Prob. 23E Ch. 1.5 - Prob. 24E Ch. 1.5 - Prob. 25E Ch. 1.5 - Prob. 26E Ch. 1.5 - Prob. 27E Ch. 1.5 - Prob. 28E Ch. 1.5 - Prob. 29E Ch. 1.5 - Prob. 30E Ch. 1.5 - Prob. 31E Ch. 1.5 - Prob. 32E Ch. 1.5 - Prob. 33E Ch. 1.5 - Prob. 34E Ch. 1.5 - Prob. 35E Ch. 1.5 - Prob. 36E Ch. 1.5 - Prob. 37E Ch. 1.5 - Prob. 38E Ch. 1.5 - Prob. 39E Ch. 1.5 - Prob. 40E Ch. 1.5 - Prob. 41E Ch. 1.5 - Prob. 42E Ch. 1.5 - Prob. 43E Ch. 1.5 - Prob. 44E Ch. 1.5 - Prob. 45E Ch. 1.5 - Prob. 46E Ch. 1.5 - Prob. 47E Ch. 1.5 - Prob. 48E Ch. 1.5 - Prob. 49E Ch. 1.5 - Prob. 50E Ch. 1.5 - Prob. 51E Ch. 1.6 - Prob. 1QR Ch. 1.6 - Prob. 2QR Ch. 1.6 - Prob. 3QR Ch. 1.6 - Prob. 4QR Ch. 1.6 - Prob. 5QR Ch. 1.6 - Prob. 6QR Ch. 1.6 - Prob. 7QR Ch. 1.6 - Prob. 8QR Ch. 1.6 - Prob. 9QR Ch. 1.6 - Prob. 10QR Ch. 1.6 - Prob. 1E Ch. 1.6 - Prob. 2E Ch. 1.6 - Prob. 3E Ch. 1.6 - 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Solution Summary: The author explains the formula and domain of the functions f+g, g(x) and cdot

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