For $f(x)=3x+1$ And $g(x)=x^2-6$, Find \[$(f+g)(x)\$\].A. $x^2+3x-5$ B. $3x^3-5$ C. $3x^2-17$ D. $x^2+3x+7$

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, using the given functions $f(x)=3x+1$ and $g(x)=x^2-6$ as examples.

What is the Sum of Two Functions?

The sum of two functions is a new function that is created by adding the corresponding terms of the two functions. In other words, if we have two functions $f(x)$ and $g(x)$, the sum of the two functions is defined as:

$$(f+g)(x) = f(x) + g(x)$$

Step 1: Identify the Functions

In this example, we are given two functions:

• $f(x) = 3x + 1$
• $g(x) = x^2 - 6$

Step 2: Add the Corresponding Terms

To find the sum of the two functions, we need to add the corresponding terms. This means that we will add the terms with the same variable (x) from both functions.

$$(f+g)(x) = (3x + 1) + (x^2 - 6)$$

Step 3: Simplify the Expression

Now that we have added the corresponding terms, we can simplify the expression by combining like terms.

$$(f+g)(x) = 3x + 1 + x^2 - 6$$

$$(f+g)(x) = x^2 + 3x - 5$$

Conclusion

In this article, we have shown how to find the sum of two functions using the given functions $f(x)=3x+1$ and $g(x)=x^2-6$ as examples. We have identified the functions, added the corresponding terms, and simplified the expression to find the sum of the two functions.

Answer

The correct answer is:

• A. $x^2+3x-5$

Final Answer

Introduction

In our previous article, we explored how to find the sum of two functions using the given functions $f(x)=3x+1$ and $g(x)=x^2-6$ as examples. In this article, we will answer some frequently asked questions about finding the sum of two functions.

Q: What is the sum of two functions?

A: The sum of two functions is a new function that is created by adding the corresponding terms of the two functions.

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

A: To find the sum of two functions, you need to:

1. Identify the functions
2. Add the corresponding terms
3. Simplify the expression by combining like terms

Q: What if the functions have different variables?

A: If the functions have different variables, you need to use the distributive property to multiply the terms with the different variables.

Q: Can I find the sum of more than two functions?

A: Yes, you can find the sum of more than two functions by adding the corresponding terms of each function.

Q: How do I know if the sum of two functions is a polynomial or not?

A: The sum of two functions is a polynomial if the resulting expression is a polynomial. A polynomial is an expression that consists of variables and coefficients, and the variables are raised to non-negative integer powers.

Q: Can I find the sum of two functions with different degrees?

A: Yes, you can find the sum of two functions with different degrees. The resulting expression will have the highest degree of the two functions.

Q: What if the sum of two functions is not a polynomial?

A: If the sum of two functions is not a polynomial, it may be a rational function, a trigonometric function, or another type of function.

Q: Can I use technology to find the sum of two functions?

A: Yes, you can use technology such as calculators or computer software to find the sum of two functions.

Q: How do I check my answer for the sum of two functions?

A: To check your answer for the sum of two functions, you can:

1. Plug in a value for the variable
2. Evaluate the expression
3. Check if the result is correct

Conclusion

In this article, we have answered some frequently asked questions about finding the sum of two functions. We have covered topics such as the definition of the sum of two functions, how to find the sum, and how to check the answer.

Final Answer

The final answer is $\boxed{yes}$, you can find the sum of two functions using the steps outlined in this article.