# The domain of f + g if the domain of f is A and the domain of g is B .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1, Problem 9RCC

(a)

To determine

## To find: The domain of f+g if the domain of f is A and the domain of g is B.

Expert Solution

Solution:

The domain of f+g is AB.

### Explanation of Solution

Express the given function as (f+g)(x)=f(x)+g(x).

The function (f+g)(x) is defined on what values the functions f(x) and g(x) are defined.

Hence, the domain of (f+g)(x) equals the intersection of the domain of f(x) and g(x).

It is given that the domain of f(x) is A and the domain of g(x) is B.

Therefore the domain of (f+g)(x) is AB.

(b)

To determine

### To find: The domain of fg if the domain of f is A and the domain of g is B.

Expert Solution

Solution:

The domain of fg is AB.

### Explanation of Solution

Express the given function as (fg)(x)=f(x)g(x).

The function (fg)(x) is defined on what values the functions f(x) and g(x) are defined.

Thus, the domain of (fg)(x) equals the intersection of the domain of f(x) and g(x).

It is given that the domain of f(x) is A and the domain of g(x) is B.

Therefore the domain of (fg)(x) is AB.

(c)

To determine

### To find: The domain of fg if the domain of f is A and the domain of g is B.

Expert Solution

Solution:

The domain of fg is AB.

### Explanation of Solution

Express the given function as (fg)(x)=f(x)g(x).

The function (fg)(x) is defined on what values the functions f(x) and g(x) are defined.

Thus, the domain of (fg)(x) equals the intersection of the domain of f(x) and g(x).

It is given that the domain of f(x) is A and the domain of g(x) is B.

Therefore the domain of (fg)(x) is AB under the condition that g(x)0.

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