# 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 34E

a.

To determine

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

Expert Solution

(fg)(x)=1x6;domain is{x|x1,x} .

### Explanation of Solution

Given:

The given function is f(x)=x,g(x)=1x3 .

Calculation:

As the given function is f(x)=x,g(x)=1x3 .

(fg)(x)=f(g(x))=1x3{as f(x)=x}=1x6

The domain of the function fg is a {x|x1,x} .

Hence,the range and domain are (fg)(x)=1x6;domain is{x|x1,x}

b.

To determine

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

Expert Solution

(gf)(x)=1x3;domain is{x|x0,x} .

### Explanation of Solution

Given:

The given function is f(x)=x,g(x)=1x3 .

Calculation:

As the given function is f(x)=x,g(x)=1x3 .

(gf)(x)=f(g(x))=1x3{as g(x)=1x3}

The domain of the function fg is a {x|x1,x} .

Hence, the range and domain are (gf)(x)=1x3;domain is{x|x0,x}

c.

To determine

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

Expert Solution

(gf)(x)=x4;domain is{x|x0,x} .

### Explanation of Solution

Given:

As the given function is f(x)=x,g(x)=1x3 .

(ff)(x)=f(g(x))=x{as f(x)=x}=x4

The domain of the function fg is a {x|x0,x} .

Hence, the range and domain are (gf)(x)=x4;domain is{x|x0,x}

d.

To determine

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

Expert Solution

(gg)(x)=11x33;domain is{x|x0,x} .

### Explanation of Solution

Given:

The given function is f(x)=x,g(x)=1x3 .

Calculation:

As the given function is f(x)=x,g(x)=1x3 .

(gg)(x)=f(g(x))=11x33{as g(x)=1x3}

The domain of the function fg is {x|x0,x} .

Hence, the range and domain are (gg)(x)=11x33;domain is{x|x0,x}

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