Understanding the Difference of Two Functions

Oct 13, 2025 by miodeya.com 99 views

Introduction

In this article, we will explore the concept of the difference of two functions and how to solve for the value of x when the difference is equal to zero. We will use the given functions f(x) = 16x - 30 and g(x) = 14x - 6 to find the value of x that satisfies the equation (f-g)(x) = 0.

Understanding the Difference of Two Functions

The difference of two functions f(x) and g(x) is defined as (f-g)(x) = f(x) - g(x). This means that we need to subtract the value of g(x) from the value of f(x) to get the difference.

Given Functions

We are given two functions:

f(x) = 16x - 30
g(x) = 14x - 6

Finding the Difference

To find the difference of the two functions, we need to subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x) = (16x - 30) - (14x - 6) = 16x - 30 - 14x + 6 = 2x - 24

Solving for x

Now that we have the difference of the two functions, we need to solve for x when the difference is equal to zero. We can set up the equation:

2x - 24 = 0

To solve for x, we can add 24 to both sides of the equation:

2x = 24

Next, we can divide both sides of the equation by 2:

x = 12

Conclusion

In this article, we have explored the concept of the difference of two functions and how to solve for the value of x when the difference is equal to zero. We used the given functions f(x) = 16x - 30 and g(x) = 14x - 6 to find the value of x that satisfies the equation (f-g)(x) = 0. The value of x that satisfies the equation is x = 12.

Answer

The correct answer is C. 12.

Additional Information

If you are having trouble understanding the concept of the difference of two functions, you can try using a graphing calculator to visualize the functions and their difference. You can also try plugging in different values of x into the equation to see how the difference changes.

References

Introduction

In our previous article, we explored the concept of the difference of two functions and how to solve for the value of x when the difference is equal to zero. We used the given functions f(x) = 16x - 30 and g(x) = 14x - 6 to find the value of x that satisfies the equation (f-g)(x) = 0. In this article, we will answer some frequently asked questions related to the topic.

Q: What is the difference of two functions?

A: The difference of two functions f(x) and g(x) is defined as (f-g)(x) = f(x) - g(x). This means that we need to subtract the value of g(x) from the value of f(x) to get the difference.

Q: How do I find the difference of two functions?

A: To find the difference of two functions, we need to subtract g(x) from f(x). We can do this by following the order of operations (PEMDAS):

Evaluate the expressions inside the parentheses.
Subtract the value of g(x) from the value of f(x).

Q: What is the equation for the difference of two functions?

A: The equation for the difference of two functions is:

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

Q: How do I solve for x when the difference is equal to zero?

A: To solve for x when the difference is equal to zero, we need to set up the equation:

(f-g)(x) = 0

We can then solve for x by following the steps outlined in our previous article.

Q: What is the value of x that satisfies the equation (f-g)(x) = 0?

A: The value of x that satisfies the equation (f-g)(x) = 0 is x = 12.

Q: Can I use a graphing calculator to visualize the functions and their difference?

A: Yes, you can use a graphing calculator to visualize the functions and their difference. This can help you understand the concept of the difference of two functions and how it changes as x varies.

Q: What are some related topics to the difference of two functions?

A: Some related topics to the difference of two functions include:

Function composition
Function inversion
Graphing functions

Conclusion

In this article, we have answered some frequently asked questions related to the difference of two functions. We hope that this article has been helpful in clarifying any confusion and providing additional information on the topic.