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Q5.

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Found in: Page 216

### Precalculus Mathematics for Calculus

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

# 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 ….

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

## 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

$\left(f+g\right)\left(x\right)\text{=}f\left(x\right)\text{}+\text{}g\left(x\right)$

## 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.