Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Let f and g be functions.
The function (f + g) (x) is defined for all values of x that are in the domains of both …. and ….
The function (fg) (x) is defined for all values of x that are in the domains of both …. and ….
The function (f/g) (x) is defined for all values of x that are in the domains of both …. and …., and g(x) is not equal to ….

The function (f + g) (x) is defined for all values of x that are in the domains of both f and g.
The function (fg) (x) is defined for all values of x that are in the domains of both f and g.
The function (f/g) (x) is defined for all values of x that are in the domains of both f and g and g(x) is not equal to 0.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part a.Step 1 – Given Information

Given that, f and g are functions.

Let us assume that f and g are the functions with domain X and Y.

Part a.Step 2 – Concept Used

The function (f + g) (x) is defined as

$(f + g) (x) = f (x) + g (x)$

Part a.Step 3 – To find the domain of (f + g) (x) for all values of x

The domain of f + g is the intersection of the domains i.e., $X \cap Y$

Therefore, we get

The function (f + g) (x) is defined for all values of x that are in the domains of both f and g.

Part b.Step 1 – Given Information

Given that, f and g are functions.

Let us assume that f and g are the functions with domain X and Y.

Part b Step 2 – Concept Used

The function (f/g) (x) is defined as

Part bStep 3 – To find the domain of (fg) (x) for all values of x

The domain of fg is the intersection of the domains i.e.,

Therefore, we get

The function (fg) (x) is defined for all values of x that are in the domains of both f and g.

Part c.Step 1 – Given Information

Given that, f and g are functions.

Let us assume that f and g are the functions with domain X and Y.

Part c.Step 2 – Concept Used

The function (f/g) (x) is defined as

Part c.Step 3 – To find the domain of (f/g) (x) for all values of x

The domain of f/g is the intersection of the domains i.e., and

Therefore, we get

The function (f/g) (x) is defined for all

values of x that are in the domains of both f and g and g(x) is not equal to 0.

Select your language

Precalculus Mathematics for Calculus

Answers without the blur.

Short Answer

Step by Step Solution

Part a.Step 1 – Given Information

Part a.Step 2 – Concept Used

Part a.Step 3 – To find the domain of (f + g) (x) for all values of x

Part b.Step 1 – Given Information

Part b Step 2 – Concept Used

Part bStep 3 – To find the domain of (fg) (x) for all values of x

Part c.Step 1 – Given Information

Part c.Step 2 – Concept Used

Part c.Step 3 – To find the domain of (f/g) (x) for all values of x

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Precalculus Mathematics for Calculus

Answers without the blur.

Short Answer

Step by Step Solution

Part a.Step 1 – Given Information

Part a.Step 2 – Concept Used

Part a.Step 3 – To find the domain of (f + g) (x) for all values of x

Part b.Step 1 – Given Information

Part b Step 2 – Concept Used

Part bStep 3 – To find the domain of (fg) (x) for all values of x

Part c.Step 1 – Given Information

Part c.Step 2 – Concept Used

Part c.Step 3 – To find the domain of (f/g) (x) for all values of x

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths