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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Solve the initial value problem: y' = x3 + y³ 3 , y(1) = 2 xy² y(x) = Hint: Notice that the equation on the right is homogeneous and see Homework exercise 23 in section 1.2 of our textbook to review techniques for solving homogeneous equations. Note that we've been given an intial value of the form y(a) = b where a > 0, so this only determines a solution corresponding to the right half of the graph of In(x), i.e., the part of the graph corresponding to positive values of x. Therefore, we should write In(x) instead of ln(|x|), since the left half of the graph is not determined by the initial condition given.

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.

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 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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