BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.3, Problem 31E

a.

To determine

To find:the given function fg and their domain.

Expert Solution

Answer to Problem 31E

  (fg)(x)=4x2+4x;domain .

Explanation of Solution

Given:

The given function is f(x)=x21,g(x)=2x+1 .

Calculation:

As the given function is f(x)=x21,g(x)=2x+1 .

The domain of the function is a real number, since both f and g are defined for all real numbers.

Now, compute the composite function directly.

  (fg)(x)=f(g(x))=(2x+1)21{as f(x)=x21}=4x2+4x+11=4x2+4x

Note thatthe domain of the function is a real numberthus, domain .

Hence,the range and domain are (fg)(x)=4x2+4x;domain

b.

To determine

To find: the given function gf and their domain.

Expert Solution

Answer to Problem 31E

  (gf)(x)=2x21;domain .

Explanation of Solution

Given:

The given function is f(x)=x21,g(x)=2x+1 .

Calculation:

As the given function is f(x)=x21,g(x)=2x+1 .

The domain of the function is a real number, since both f and g are defined for all real numbers.

Now, compute the composite function directly.

  (gf)(x)=g(f(x))=2(x21)+1{as g(x)=2x+1}=2x22+1=2x21

Note thatthe domain of the function is a real numberthus, domain .

Hence, the range and domain are (gf)(x)=2x21;domain

c.

To determine

To find: the given function ff and their domain.

Expert Solution

Answer to Problem 31E

  (ff)(x)=x42x2;domain .

Explanation of Solution

Given:

The given function is f(x)=x21,g(x)=2x+1 .

Calculation:

As the given function is f(x)=x21,g(x)=2x+1 .

The domain of the function is a real number, since both f and g are defined for all real numbers.

Now, compute the composite function directly.

  (ff)(x)=g(f(x))=(x21)21{as f(x)=x21}=x42x2+11=x42x2

Note thatthe domain of the function is a real numberthus, domain .

Hence, the range and domain are (ff)(x)=x42x2;domain

d.

To determine

To find: the given function gg and their domain.

Expert Solution

Answer to Problem 31E

  (gg)(x)=4x+3;domain .

Explanation of Solution

Given:

The given function is f(x)=x21,g(x)=2x+1 .

Calculation:

As the given function is f(x)=x21,g(x)=2x+1 .

The domain of the function is a real number, since both f and g are defined for all real numbers.

Now, compute the composite function directly.

  (gg)(x)=g(f(x))=2(2x+1)+1{as g(x)=2x+1}=4x+2+1=4x+3

Note thatthe domain of the function is a real numberthus, domain .

Hence, the range and domain are (gg)(x)=4x+3;domain

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!