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Q5.

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Precalculus Mathematics for Calculus
Found in: Page 216
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

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Short Answer

Let f and g be functions.

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

  3. 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 ….

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

  3. 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

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+gx = fx + gx

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.,XY

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.

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