Given:${ \begin{array}{l} f(x) = 2x - 1 \ g(x) = 7x \end{array} }$Find { (f+g)(x)$}$.A. ${ 9x - 1\$} B. ${ 14x - 1\$} C. ${ 14x^2 - 7x\$} D. ${ 2x - 6x\$}

Introduction

In mathematics, functions are used to describe relationships between variables. When we have two functions, we can combine them to create a new function. In this article, we will explore how to find the sum of two functions, specifically the functions f(x) and g(x). We will use the given functions f(x) = 2x - 1 and g(x) = 7x to demonstrate the process.

Understanding the Concept of Function Summation

The summation of two functions, f(x) and g(x), is denoted as (f+g)(x). This new function is created by adding the corresponding terms of the two original functions. In other words, we add the x-term of f(x) to the x-term of g(x), and the constant term of f(x) to the constant term of g(x).

Step-by-Step Solution

To find the sum of the two functions f(x) = 2x - 1 and g(x) = 7x, we will follow these steps:

Step 1: Identify the x-term and constant term of each function

The x-term of f(x) is 2x, and the constant term is -1. The x-term of g(x) is 7x, and the constant term is 0 (since there is no constant term in g(x)).

Step 2: Add the x-terms of the two functions

We add the x-term of f(x) (2x) to the x-term of g(x) (7x) to get 2x + 7x = 9x.

Step 3: Add the constant terms of the two functions

We add the constant term of f(x) (-1) to the constant term of g(x) (0) to get -1 + 0 = -1.

Step 4: Combine the x-term and constant term to form the new function

We combine the x-term (9x) and the constant term (-1) to form the new function (f+g)(x) = 9x - 1.

Conclusion

In conclusion, the sum of the two functions f(x) = 2x - 1 and g(x) = 7x is (f+g)(x) = 9x - 1. This new function is created by adding the corresponding terms of the two original functions.

Answer

The correct answer is A. 9x - 1.

Discussion

This problem demonstrates the concept of function summation, which is an important concept in mathematics. By understanding how to find the sum of two functions, we can apply this knowledge to solve a wide range of problems in mathematics and other fields.

Real-World Applications

The concept of function summation has many real-world applications. For example, in economics, the sum of two functions can be used to model the relationship between two variables, such as the demand for a product and the supply of a product. In physics, the sum of two functions can be used to model the motion of an object, such as the position and velocity of an object.

Tips and Tricks

When finding the sum of two functions, make sure to identify the x-term and constant term of each function. Then, add the x-terms and constant terms separately to form the new function. Finally, combine the x-term and constant term to form the new function.

Common Mistakes

When finding the sum of two functions, make sure to avoid common mistakes such as:

• Adding the x-term and constant term of one function to the x-term and constant term of the other function separately.
• Forgetting to add the constant term of one function to the constant term of the other function.
• Not combining the x-term and constant term to form the new function.

Conclusion

Introduction

In our previous article, we explored how to find the sum of two functions, specifically the functions f(x) = 2x - 1 and g(x) = 7x. We demonstrated the process of adding the corresponding terms of the two original functions to create a new function. In this article, we will answer some frequently asked questions about finding the sum of two functions.

Q: What is the difference between adding two functions and multiplying two functions?

A: When adding two functions, we add the corresponding terms of the two original functions. When multiplying two functions, we multiply the two functions together, using the distributive property to expand the product.

Q: How do I know which terms to add when finding the sum of two functions?

A: When finding the sum of two functions, you should add the x-term of one function to the x-term of the other function, and the constant term of one function to the constant term of the other function.

Q: What if one of the functions has a constant term and the other function does not?

A: If one of the functions has a constant term and the other function does not, you should still add the constant term of the function with the constant term to the constant term of the other function.

Q: Can I add more than two functions together?

A: Yes, you can add more than two functions together. The process is the same as adding two functions: add the corresponding terms of the two original functions.

Q: How do I know if the sum of two functions is a linear function or a quadratic function?

A: If the sum of two functions is a linear function, it will have a constant slope and a constant y-intercept. If the sum of two functions is a quadratic function, it will have a variable slope and a variable y-intercept.

Q: Can I use the sum of two functions to model real-world phenomena?

A: Yes, you can use the sum of two functions to model real-world phenomena. For example, you can use the sum of two functions to model the relationship between two variables, such as the demand for a product and the supply of a product.

Q: How do I apply the concept of function summation to solve problems in other fields?

A: The concept of function summation can be applied to solve problems in other fields, such as economics, physics, and engineering. For example, you can use the sum of two functions to model the motion of an object, or to model the relationship between two variables.

Q: What are some common mistakes to avoid when finding the sum of two functions?

A: Some common mistakes to avoid when finding the sum of two functions include:

• Adding the x-term and constant term of one function to the x-term and constant term of the other function separately.
• Forgetting to add the constant term of one function to the constant term of the other function.
• Not combining the x-term and constant term to form the new function.

Conclusion

In conclusion, finding the sum of two functions is an important concept in mathematics. By understanding how to find the sum of two functions, we can apply this knowledge to solve a wide range of problems in mathematics and other fields.