# the given function f ∘ g and their domain.

### 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 1.3, Problem 33E

a.

To determine

## To find:the given function f∘g and their domain.

Expert Solution

(fg)(x)=13cosx;domain .

### Explanation of Solution

Given:

The given function is f(x)=13x,g(x)=cosx .

Calculation:

As the given function is f(x)=13x,g(x)=cosx .

(fg)(x)=f(g(x))=13cosx{as f(x)=13x}

Note that the domain of the function is a polynomial function thus, domain .

Hence,the range and domain are (fg)(x)=13cosx;domain

b.

To determine

### To find: the given function g∘f and their domain.

Expert Solution

(gf)(x)=cos(13x);domain .

### Explanation of Solution

Given:

The given function is f(x)=13x,g(x)=cosx .

Calculation:

As the given function is f(x)=13x,g(x)=cosx .

(gf)(x)=f(g(x))=cos(13x){as g(x)=cosx}

Note that the domain of the function is a polynomial function thus, domain .

Hence, the range and domain are (gf)(x)=cos(13x);domain

c.

To determine

### To find: the given function f∘f and their domain.

Expert Solution

(ff)(x)=9x2;domain .

### Explanation of Solution

Given:

The given function is f(x)=13x,g(x)=cosx .

Calculation:

As the given function is f(x)=13x,g(x)=cosx .

(ff)(x)=f(f(x))=13(13x){as g(x)=cosx}=13+9x=9x2

Note that the domain of the function is a polynomial function thus, domain .

Hence, the range and domain are (ff)(x)=9x2;domain

d.

To determine

### To find: the given function g∘g and their domain.

Expert Solution

(gg)(x)=cos(cosx);domain .

### Explanation of Solution

Given:

The given function is f(x)=13x,g(x)=cosx .

Calculation:

As the given function is f(x)=13x,g(x)=cosx .

(gg)(x)=f(g(x))=cos(cosx){as g(x)=cosx}

Note that the domain of the function is a polynomial function thus, domain .

Hence, the range and domain are (gg)(x)=cos(cosx);domain

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