For the product of the functions F ( x ) = x 2 + 1 and H ( x ) = − x + 1 , the values at x = − 2 , x = − 1 , x = 0 , x = 1 and x = 2 , graph component piece functions and their product.

Question

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Answer 1

Question

Chapter 1.2, Problem 24E

To determine

To calculate: For the product of the functions F(x)=x2+1 and H(x)=−x+1 , the values at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 24E

The value of the functions and product of the functions for different values of x are,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

The graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 1

Explanation of Solution

Given information:

The functions, F(x)=x2+1 and H(x)=−x+1 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, F(x)=x2+1 and H(x)=−x+1 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of F(x)⋅H(x) that is product of the functions,

F(x)⋅H(x)=(x2+1)⋅(−x+1)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

F(x)⋅H(x)=(x2+1)⋅(−x+1)=x2(−x+1)+1(−x+1)=−x3+x2−x+1

Therefore, the value of sum of the function is −x3+x2−x+1

x2−x+2 .

Now, evaluate the value of the individual function F(x)=x2+1 , H(x)=−x+1 and product of the function, F(x)⋅H(x)=−x3+x2−x+1 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−2)=(−2)2+1=4+1=5

Next,

H(−2)=−(−2)+1=3

Last,

F(−2)⋅H(−2)=−(−2)3+(−2)2−(−2)+1=8+4+2+1=15

For x=−1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−1)=(−1)2+1=1+1=2

Next,

H(−1)=−(−1)+1=2

Last,

F(−1)⋅H(−1)=−(−1)3+(−1)2−(−1)+1=1+1+1+1=4

For x=0 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(0)=(0)2+1=1

Next,

H(0)=0+1=1

Last,

F(0)⋅H(0)=−(0)3+(0)2−(0)+1=1

For x=1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(1)=(1)2+1=2

Next,

H(1)=−1+1=0

Last,

F(1)⋅H(1)=−(1)3+(1)2−(1)+1=−1+1−1+1=0

For x=2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(2)=(2)2+1=4+1=5

Next,

H(2)=−2+1=−1

Last,

F(2)⋅H(2)=−(2)3+(2)2−(2)+1=−8+4−2+1=−5

Thus, the above results are tabulated as,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

Plot the graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

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Answer 2

Question

Chapter 1.2, Problem 24E

To determine

To calculate: For the product of the functions F(x)=x2+1 and H(x)=−x+1 , the values at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 24E

The value of the functions and product of the functions for different values of x are,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

The graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 1

Explanation of Solution

Given information:

The functions, F(x)=x2+1 and H(x)=−x+1 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, F(x)=x2+1 and H(x)=−x+1 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of F(x)⋅H(x) that is product of the functions,

F(x)⋅H(x)=(x2+1)⋅(−x+1)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

F(x)⋅H(x)=(x2+1)⋅(−x+1)=x2(−x+1)+1(−x+1)=−x3+x2−x+1

Therefore, the value of sum of the function is −x3+x2−x+1

x2−x+2 .

Now, evaluate the value of the individual function F(x)=x2+1 , H(x)=−x+1 and product of the function, F(x)⋅H(x)=−x3+x2−x+1 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−2)=(−2)2+1=4+1=5

Next,

H(−2)=−(−2)+1=3

Last,

F(−2)⋅H(−2)=−(−2)3+(−2)2−(−2)+1=8+4+2+1=15

For x=−1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−1)=(−1)2+1=1+1=2

Next,

H(−1)=−(−1)+1=2

Last,

F(−1)⋅H(−1)=−(−1)3+(−1)2−(−1)+1=1+1+1+1=4

For x=0 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(0)=(0)2+1=1

Next,

H(0)=0+1=1

Last,

F(0)⋅H(0)=−(0)3+(0)2−(0)+1=1

For x=1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(1)=(1)2+1=2

Next,

H(1)=−1+1=0

Last,

F(1)⋅H(1)=−(1)3+(1)2−(1)+1=−1+1−1+1=0

For x=2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(2)=(2)2+1=4+1=5

Next,

H(2)=−2+1=−1

Last,

F(2)⋅H(2)=−(2)3+(2)2−(2)+1=−8+4−2+1=−5

Thus, the above results are tabulated as,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

Plot the graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 1.2, Problem 24E

To determine

To calculate: For the product of the functions F(x)=x2+1 and H(x)=−x+1 , the values at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 24E

The value of the functions and product of the functions for different values of x are,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

The graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 1

Explanation of Solution

Given information:

The functions, F(x)=x2+1 and H(x)=−x+1 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, F(x)=x2+1 and H(x)=−x+1 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of F(x)⋅H(x) that is product of the functions,

F(x)⋅H(x)=(x2+1)⋅(−x+1)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

F(x)⋅H(x)=(x2+1)⋅(−x+1)=x2(−x+1)+1(−x+1)=−x3+x2−x+1

Therefore, the value of sum of the function is −x3+x2−x+1

x2−x+2 .

Now, evaluate the value of the individual function F(x)=x2+1 , H(x)=−x+1 and product of the function, F(x)⋅H(x)=−x3+x2−x+1 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−2)=(−2)2+1=4+1=5

Next,

H(−2)=−(−2)+1=3

Last,

F(−2)⋅H(−2)=−(−2)3+(−2)2−(−2)+1=8+4+2+1=15

For x=−1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−1)=(−1)2+1=1+1=2

Next,

H(−1)=−(−1)+1=2

Last,

F(−1)⋅H(−1)=−(−1)3+(−1)2−(−1)+1=1+1+1+1=4

For x=0 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(0)=(0)2+1=1

Next,

H(0)=0+1=1

Last,

F(0)⋅H(0)=−(0)3+(0)2−(0)+1=1

For x=1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(1)=(1)2+1=2

Next,

H(1)=−1+1=0

Last,

F(1)⋅H(1)=−(1)3+(1)2−(1)+1=−1+1−1+1=0

For x=2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(2)=(2)2+1=4+1=5

Next,

H(2)=−2+1=−1

Last,

F(2)⋅H(2)=−(2)3+(2)2−(2)+1=−8+4−2+1=−5

Thus, the above results are tabulated as,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

Plot the graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 1.2, Problem 24E

To determine

To calculate: For the product of the functions F(x)=x2+1 and H(x)=−x+1 , the values at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 24E

The value of the functions and product of the functions for different values of x are,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

The graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 1

Explanation of Solution

Given information:

The functions, F(x)=x2+1 and H(x)=−x+1 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, F(x)=x2+1 and H(x)=−x+1 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of F(x)⋅H(x) that is product of the functions,

F(x)⋅H(x)=(x2+1)⋅(−x+1)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

F(x)⋅H(x)=(x2+1)⋅(−x+1)=x2(−x+1)+1(−x+1)=−x3+x2−x+1

Therefore, the value of sum of the function is −x3+x2−x+1

x2−x+2 .

Now, evaluate the value of the individual function F(x)=x2+1 , H(x)=−x+1 and product of the function, F(x)⋅H(x)=−x3+x2−x+1 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−2)=(−2)2+1=4+1=5

Next,

H(−2)=−(−2)+1=3

Last,

F(−2)⋅H(−2)=−(−2)3+(−2)2−(−2)+1=8+4+2+1=15

For x=−1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−1)=(−1)2+1=1+1=2

Next,

H(−1)=−(−1)+1=2

Last,

F(−1)⋅H(−1)=−(−1)3+(−1)2−(−1)+1=1+1+1+1=4

For x=0 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(0)=(0)2+1=1

Next,

H(0)=0+1=1

Last,

F(0)⋅H(0)=−(0)3+(0)2−(0)+1=1

For x=1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(1)=(1)2+1=2

Next,

H(1)=−1+1=0

Last,

F(1)⋅H(1)=−(1)3+(1)2−(1)+1=−1+1−1+1=0

For x=2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(2)=(2)2+1=4+1=5

Next,

H(2)=−2+1=−1

Last,

F(2)⋅H(2)=−(2)3+(2)2−(2)+1=−8+4−2+1=−5

Thus, the above results are tabulated as,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

Plot the graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 1.2, Problem 24E

To determine

To calculate: For the product of the functions F(x)=x2+1 and H(x)=−x+1 , the values at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 24E

The value of the functions and product of the functions for different values of x are,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

The graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 1

Explanation of Solution

Given information:

The functions, F(x)=x2+1 and H(x)=−x+1 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, F(x)=x2+1 and H(x)=−x+1 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of F(x)⋅H(x) that is product of the functions,

F(x)⋅H(x)=(x2+1)⋅(−x+1)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

F(x)⋅H(x)=(x2+1)⋅(−x+1)=x2(−x+1)+1(−x+1)=−x3+x2−x+1

Therefore, the value of sum of the function is −x3+x2−x+1

x2−x+2 .

Now, evaluate the value of the individual function F(x)=x2+1 , H(x)=−x+1 and product of the function, F(x)⋅H(x)=−x3+x2−x+1 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−2)=(−2)2+1=4+1=5

Next,

H(−2)=−(−2)+1=3

Last,

F(−2)⋅H(−2)=−(−2)3+(−2)2−(−2)+1=8+4+2+1=15

For x=−1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−1)=(−1)2+1=1+1=2

Next,

H(−1)=−(−1)+1=2

Last,

F(−1)⋅H(−1)=−(−1)3+(−1)2−(−1)+1=1+1+1+1=4

For x=0 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(0)=(0)2+1=1

Next,

H(0)=0+1=1

Last,

F(0)⋅H(0)=−(0)3+(0)2−(0)+1=1

For x=1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(1)=(1)2+1=2

Next,

H(1)=−1+1=0

Last,

F(1)⋅H(1)=−(1)3+(1)2−(1)+1=−1+1−1+1=0

For x=2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(2)=(2)2+1=4+1=5

Next,

H(2)=−2+1=−1

Last,

F(2)⋅H(2)=−(2)3+(2)2−(2)+1=−8+4−2+1=−5

Thus, the above results are tabulated as,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

Plot the graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

Answer 6

Chapter 1.2, Problem 24E

To determine

To calculate: For the product of the functions F(x)=x2+1 and H(x)=−x+1 , the values at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 24E

The value of the functions and product of the functions for different values of x are,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

The graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 1

Explanation of Solution

Given information:

The functions, F(x)=x2+1 and H(x)=−x+1 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, F(x)=x2+1 and H(x)=−x+1 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of F(x)⋅H(x) that is product of the functions,

F(x)⋅H(x)=(x2+1)⋅(−x+1)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

F(x)⋅H(x)=(x2+1)⋅(−x+1)=x2(−x+1)+1(−x+1)=−x3+x2−x+1

Therefore, the value of sum of the function is −x3+x2−x+1

x2−x+2 .

Now, evaluate the value of the individual function F(x)=x2+1 , H(x)=−x+1 and product of the function, F(x)⋅H(x)=−x3+x2−x+1 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−2)=(−2)2+1=4+1=5

Next,

H(−2)=−(−2)+1=3

Last,

F(−2)⋅H(−2)=−(−2)3+(−2)2−(−2)+1=8+4+2+1=15

For x=−1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−1)=(−1)2+1=1+1=2

Next,

H(−1)=−(−1)+1=2

Last,

F(−1)⋅H(−1)=−(−1)3+(−1)2−(−1)+1=1+1+1+1=4

For x=0 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(0)=(0)2+1=1

Next,

H(0)=0+1=1

Last,

F(0)⋅H(0)=−(0)3+(0)2−(0)+1=1

For x=1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(1)=(1)2+1=2

Next,

H(1)=−1+1=0

Last,

F(1)⋅H(1)=−(1)3+(1)2−(1)+1=−1+1−1+1=0

For x=2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(2)=(2)2+1=4+1=5

Next,

H(2)=−2+1=−1

Last,

F(2)⋅H(2)=−(2)3+(2)2−(2)+1=−8+4−2+1=−5

Thus, the above results are tabulated as,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

Plot the graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

Answer 7

Chapter 1.2, Problem 24E

To determine

To calculate: For the product of the functions F(x)=x2+1 and H(x)=−x+1 , the values at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Answer 8

Expert Solution & Answer

Answer to Problem 24E

The value of the functions and product of the functions for different values of x are,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

The graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 1

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given information:

The functions, F(x)=x2+1 and H(x)=−x+1 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, F(x)=x2+1 and H(x)=−x+1 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of F(x)⋅H(x) that is product of the functions,

F(x)⋅H(x)=(x2+1)⋅(−x+1)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

F(x)⋅H(x)=(x2+1)⋅(−x+1)=x2(−x+1)+1(−x+1)=−x3+x2−x+1

Therefore, the value of sum of the function is −x3+x2−x+1

x2−x+2 .

Now, evaluate the value of the individual function F(x)=x2+1 , H(x)=−x+1 and product of the function, F(x)⋅H(x)=−x3+x2−x+1 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−2)=(−2)2+1=4+1=5

Next,

H(−2)=−(−2)+1=3

Last,

F(−2)⋅H(−2)=−(−2)3+(−2)2−(−2)+1=8+4+2+1=15

For x=−1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(−1)=(−1)2+1=1+1=2

Next,

H(−1)=−(−1)+1=2

Last,

F(−1)⋅H(−1)=−(−1)3+(−1)2−(−1)+1=1+1+1+1=4

For x=0 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(0)=(0)2+1=1

Next,

H(0)=0+1=1

Last,

F(0)⋅H(0)=−(0)3+(0)2−(0)+1=1

For x=1 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(1)=(1)2+1=2

Next,

H(1)=−1+1=0

Last,

F(1)⋅H(1)=−(1)3+(1)2−(1)+1=−1+1−1+1=0

For x=2 , substitute the value of x in the functions, F(x)=x2+1 , H(x)=−x+1 and F(x)⋅H(x)=−x3+x2−x+1 .

F(2)=(2)2+1=4+1=5

Next,

H(2)=−2+1=−1

Last,

F(2)⋅H(2)=−(2)3+(2)2−(2)+1=−8+4−2+1=−5

Thus, the above results are tabulated as,

xF(x)H(x)( F⋅H)(x)−25315−12240111120025−1−5

Plot the graph of the functions F(x)=x2+1 , H(x)=−x+1 and (F⋅H)(x)=−x3+x2−x+1 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 24E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

Answer 12

Ch. 1.2 - Identify the variables and parameters in the...Ch. 1.2 - Prob. 2E Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...

For the product of the functions F ( x ) = x 2 + 1 and H ( x ) = − x + 1 , the values at x = − 2 , x = − 1 , x = 0 , x = 1 and x = 2 , graph component piece functions and their product.

To calculate: For the product of the functions F(x)=x2+1 and H(x)=−x+1 , the values at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Answer to Problem 24E

Explanation of Solution

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