If F ( X ) = 16 X − 30 F(x) = 16x - 30 F ( X ) = 16 X − 30 And G ( X ) = 14 X − 6 G(x) = 14x - 6 G ( X ) = 14 X − 6 , For Which Value Of X X X Does ( F − G ) ( X ) = 0 (f-g)(x) = 0 ( F − G ) ( X ) = 0 ?A. − 18 -18 − 18 B. − 12 -12 − 12 C. 12 12 12 D. 18 18 18
Introduction
In mathematics, functions are used to describe the relationship between variables. When we have two functions, we can find the difference between them by subtracting one function from the other. In this article, we will explore how to find the value of x for which the difference of two functions is equal to zero.
Understanding the Functions
We are given two functions:
- f(x) = 16x - 30
- g(x) = 14x - 6
These functions are linear, meaning they have a constant slope. The first function, f(x), has a slope of 16 and a y-intercept of -30. The second function, g(x), has a slope of 14 and a y-intercept of -6.
Finding the Difference of the Functions
To find the difference of the two functions, we subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x)
(f-g)(x) = (16x - 30) - (14x - 6)
(f-g)(x) = 16x - 30 - 14x + 6
(f-g)(x) = 2x - 24
Solving for x
Now that we have the difference of the two functions, we want to find the value of x for which (f-g)(x) is equal to zero. We can set up an equation and solve for x:
(f-g)(x) = 0
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 found the value of x for which the difference of two functions is equal to zero. We started by understanding the two functions, f(x) and g(x), and then found the difference of the functions. Finally, we solved for x by setting the difference equal to zero and solving for x. The value of x that we found is x = 12.
Final Answer
The final answer is x = 12.
Discussion
This problem is a great example of how to find the difference of two functions and solve for x. It requires a basic understanding of linear functions and algebraic manipulation. If you have any questions or would like to see more examples, please let us know in the comments below.
Related Topics
- Linear Functions: Linear functions are functions that have a constant slope. They can be represented in the form f(x) = mx + b, where m is the slope and b is the y-intercept.
- Algebraic Manipulation: Algebraic manipulation involves using mathematical operations to simplify or solve equations. In this problem, we used addition and subtraction to simplify the difference of the two functions.
- Solving Equations: Solving equations involves finding the value of a variable that makes the equation true. In this problem, we solved for x by setting the difference of the two functions equal to zero and solving for x.
Practice Problems
- Find the difference of the two functions f(x) = 3x + 2 and g(x) = 2x - 1.
- Solve for x in the equation (f-g)(x) = 0, where f(x) = 5x - 3 and g(x) = 3x + 2.
- Find the value of x for which the difference of the two functions f(x) = 2x + 1 and g(x) = x - 2 is equal to zero.
Introduction
In our previous article, we explored how to find the value of x for which the difference of two functions is equal to zero. We used the functions f(x) = 16x - 30 and g(x) = 14x - 6 to demonstrate the concept. In this article, we will answer some frequently asked questions about solving for the value of x in the difference of two functions.
Q: What is the difference of two functions?
A: The difference of two functions is the result of subtracting one function from the other. It is denoted by (f-g)(x) or (g-f)(x).
Q: How do I find the difference of two functions?
A: To find the difference of two functions, you can subtract the second function from the first function. For example, if we have f(x) = 16x - 30 and g(x) = 14x - 6, the difference of the two functions is (f-g)(x) = (16x - 30) - (14x - 6).
Q: How do I solve for x in the difference of two functions?
A: To solve for x in the difference of two functions, you can set the difference equal to zero and solve for x. For example, if we have (f-g)(x) = 2x - 24, we can set it equal to zero and solve for x: 2x - 24 = 0.
Q: What if the difference of the two functions is not equal to zero?
A: If the difference of the two functions is not equal to zero, it means that the two functions are not equal at that point. In this case, you can try to find the value of x for which the difference of the two functions is equal to a specific value, such as 0 or 1.
Q: Can I use this method to solve for x in any type of function?
A: No, this method is only applicable to linear functions. If you have a non-linear function, you will need to use a different method to solve for x.
Q: How do I know if the value of x I found is correct?
A: To verify the value of x you found, you can plug it back into the original equation and check if it is true. If it is true, then the value of x you found is correct.
Q: Can I use a calculator to solve for x?
A: Yes, you can use a calculator to solve for x. However, it's always a good idea to check your work by plugging the value of x back into the original equation.
Q: What if I get stuck or don't understand the concept?
A: Don't worry! If you get stuck or don't understand the concept, you can try re-reading the article or seeking help from a teacher or tutor.
Conclusion
Solving for the value of x in the difference of two functions is a fundamental concept in algebra. By following the steps outlined in this article, you can find the value of x for which the difference of two functions is equal to zero. Remember to always check your work and seek help if you need it.
Final Answer
The final answer is x = 12.
Discussion
This article is a great resource for anyone who wants to learn how to solve for the value of x in the difference of two functions. If you have any questions or would like to see more examples, please let us know in the comments below.
Related Topics
- Linear Functions: Linear functions are functions that have a constant slope. They can be represented in the form f(x) = mx + b, where m is the slope and b is the y-intercept.
- Algebraic Manipulation: Algebraic manipulation involves using mathematical operations to simplify or solve equations. In this problem, we used addition and subtraction to simplify the difference of the two functions.
- Solving Equations: Solving equations involves finding the value of a variable that makes the equation true. In this problem, we solved for x by setting the difference of the two functions equal to zero and solving for x.
Practice Problems
- Find the difference of the two functions f(x) = 3x + 2 and g(x) = 2x - 1.
- Solve for x in the equation (f-g)(x) = 0, where f(x) = 5x - 3 and g(x) = 3x + 2.
- Find the value of x for which the difference of the two functions f(x) = 2x + 1 and g(x) = x - 2 is equal to zero.