Properties of Function Subtraction

Oct 13, 2025 by miodeya.com 11 views

Suppose that the Functions r(x) and s(x) are Defined for All Real Numbers x

In this article, we will explore the concept of function subtraction and how it can be applied to two given functions, r(x) and s(x). The functions r(x) and s(x) are defined as follows:

r(x) = 2x - 6 s(x) = 4x

We will write the expressions for (r-s)(x) and discuss the properties of function subtraction.

Function subtraction is a fundamental concept in mathematics that involves subtracting one function from another. Given two functions f(x) and g(x), the function subtraction (f-g)(x) is defined as:

(f-g)(x) = f(x) - g(x)

In this case, we have two functions r(x) and s(x), and we want to find the expression for (r-s)(x).

Writing the Expression for (r-s)(x)

To write the expression for (r-s)(x), we simply subtract the function s(x) from the function r(x):

(r-s)(x) = r(x) - s(x) = (2x - 6) - (4x) = 2x - 6 - 4x = -2x - 6

Therefore, the expression for (r-s)(x) is -2x - 6.

Properties of Function Subtraction

Function subtraction has several properties that are important to understand. Some of these properties include:

Closure: The result of subtracting two functions is always a function.
Associativity: The order in which we subtract functions does not affect the result. For example, (f-g)(x) = (f-h)(x) - g(x) = f(x) - (h(x) - g(x)).
Distributivity: The subtraction of functions can be distributed over addition. For example, (f-g)(x) + (f-h)(x) = (f-f)(x) + (g-h)(x) = 0 + (g-h)(x) = g(x) - h(x).

Real-World Applications of Function Subtraction

Function subtraction has several real-world applications, including:

Physics: In physics, function subtraction is used to describe the motion of objects. For example, the position of an object at time t can be described by the function x(t) = v0t + x0, where v0 is the initial velocity and x0 is the initial position. The velocity of the object can be described by the function v(t) = x'(t) = v0. The acceleration of the object can be described by the function a(t) = v'(t) = 0.
Economics: In economics, function subtraction is used to describe the relationship between two variables. For example, the demand for a product can be described by the function D(x) = px - c, where p is the price of the product and c is the cost of production. The supply of the product can be described by the function S(x) = mx + b, where m is the slope of the supply curve and b is the y-intercept. The equilibrium price and quantity can be described by the function E(x) = D(x) - S(x).

In this article, we have explored the concept of function subtraction and how it can be applied to two given functions, r(x) and s(x). We have written the expression for (r-s)(x) and discussed the properties of function subtraction. We have also discussed the real-world applications of function subtraction in physics and economics.
Suppose that the Functions r(x) and s(x) are Defined for All Real Numbers x: Q&A

In our previous article, we explored the concept of function subtraction and how it can be applied to two given functions, r(x) and s(x). We wrote the expression for (r-s)(x) and discussed the properties of function subtraction. In this article, we will answer some frequently asked questions about function subtraction and provide additional examples to help solidify your understanding.

Q: What is function subtraction?

A: Function subtraction is a fundamental concept in mathematics that involves subtracting one function from another. Given two functions f(x) and g(x), the function subtraction (f-g)(x) is defined as:

(f-g)(x) = f(x) - g(x)

Q: How do I write the expression for (r-s)(x)?

A: To write the expression for (r-s)(x), you simply subtract the function s(x) from the function r(x):

(r-s)(x) = r(x) - s(x) = (2x - 6) - (4x) = 2x - 6 - 4x = -2x - 6

Q: What are some properties of function subtraction?

A: Function subtraction has several properties that are important to understand. Some of these properties include:

Closure: The result of subtracting two functions is always a function.
Associativity: The order in which we subtract functions does not affect the result. For example, (f-g)(x) = (f-h)(x) - g(x) = f(x) - (h(x) - g(x)).
Distributivity: The subtraction of functions can be distributed over addition. For example, (f-g)(x) + (f-h)(x) = (f-f)(x) + (g-h)(x) = 0 + (g-h)(x) = g(x) - h(x).

Q: What are some real-world applications of function subtraction?

A: Function subtraction has several real-world applications, including:

Physics: In physics, function subtraction is used to describe the motion of objects. For example, the position of an object at time t can be described by the function x(t) = v0t + x0, where v0 is the initial velocity and x0 is the initial position. The velocity of the object can be described by the function v(t) = x'(t) = v0. The acceleration of the object can be described by the function a(t) = v'(t) = 0.
Economics: In economics, function subtraction is used to describe the relationship between two variables. For example, the demand for a product can be described by the function D(x) = px - c, where p is the price of the product and c is the cost of production. The supply of the product can be described by the function S(x) = mx + b, where m is the slope of the supply curve and b is the y-intercept. The equilibrium price and quantity can be described by the function E(x) = D(x) - S(x).

Q: Can I use function subtraction with different types of functions?

A: Yes, you can use function subtraction with different types of functions, including polynomial functions, rational functions, and trigonometric functions. However, you must ensure that the functions are defined for all real numbers x.

Q: How do I evaluate the expression for (r-s)(x) at a specific value of x?

A: To evaluate the expression for (r-s)(x) at a specific value of x, you simply substitute the value of x into the expression:

(r-s)(x) = -2x - 6 (r-s)(3) = -2(3) - 6 = -6 - 6 = -12

In this article, we have answered some frequently asked questions about function subtraction and provided additional examples to help solidify your understanding. We hope that this article has been helpful in clarifying the concept of function subtraction and its applications.