If F ( X ) = 3 X + 10 X F(x)=3^x+10x F ( X ) = 3 X + 10 X And G ( X ) = 4 X − 2 G(x)=4x-2 G ( X ) = 4 X − 2 , Find ( F − G ) ( X (f-g)(x ( F − G ) ( X ].A. 17 X − 2 17x-2 17 X − 2 B. 3 X + 6 X + 2 3^x+6x+2 3 X + 6 X + 2 C. 3 X − 6 X + 2 3^x-6x+2 3 X − 6 X + 2 D. 3 X + 14 X − 2 3^x+14x-2 3 X + 14 X − 2

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Understanding the Problem

To find the difference between two functions, we need to subtract the second function from the first function. In this case, we are given two functions, $f(x)$ and $g(x)$, and we need to find the difference between them, denoted as $(f-g)(x)$.

Step 1: Write Down the Functions

The first function is $f(x)=3^x+10x$, and the second function is $g(x)=4x-2$.

Step 2: Subtract the Second Function from the First Function

To find the difference between the two functions, we need to subtract the second function from the first function. This can be done by subtracting the corresponding terms of the two functions.

Step 3: Perform the Subtraction

We can start by subtracting the terms of the second function from the terms of the first function.

$(f-g)(x) = (3^x+10x) - (4x-2)$

Step 4: Simplify the Expression

Now, we can simplify the expression by combining like terms.

$(f-g)(x) = 3^x + 10x - 4x + 2$

Step 5: Combine Like Terms

We can combine the like terms, $10x$ and $-4x$, to get $6x$.

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

Step 6: Check the Answer Choices

Now, we can check the answer choices to see which one matches our result.

Conclusion

Based on our calculation, we can see that the correct answer is:

B. $3^x+6x+2$

This is the difference between the two functions, $(f-g)(x)$.

Final Answer

The final answer is $\boxed{3^x+6x+2}$.

Discussion

This problem requires us to understand the concept of function subtraction and how to perform it. We need to be able to subtract the corresponding terms of the two functions and combine like terms to simplify the expression. This problem also requires us to be able to check the answer choices and select the correct one.

Related Problems

If you want to practice more problems like this, you can try the following:

• Find $(f+g)(x)$ if $f(x)=3^x+10x$ and $g(x)=4x-2$.
• Find $(f-g)(x)$ if $f(x)=2x^2+3x$ and $g(x)=x^2-2x$.
• Find $(f+g)(x)$ if $f(x)=x^2+2x$ and $g(x)=x^2-3x$.

Tips and Tricks

When subtracting functions, make sure to subtract the corresponding terms of the two functions. Also, be careful when combining like terms, as this can affect the final result.

Common Mistakes

One common mistake when subtracting functions is to forget to subtract the corresponding terms of the two functions. Another common mistake is to combine like terms incorrectly, which can affect the final result.

Real-World Applications

Function subtraction has many real-world applications, such as in physics and engineering. For example, when calculating the difference between two physical quantities, such as velocity and acceleration, we need to subtract the corresponding terms of the two quantities.

Conclusion

In conclusion, function subtraction is an important concept in mathematics that requires us to understand how to subtract the corresponding terms of two functions and combine like terms to simplify the expression. This problem requires us to be able to perform function subtraction and check the answer choices to select the correct one.

Introduction

Function subtraction is a fundamental concept in mathematics that requires us to understand how to subtract the corresponding terms of two functions and combine like terms to simplify the expression. In this article, we will answer some common questions related to function subtraction.

Q1: What is function subtraction?

A1: Function subtraction is the process of subtracting one function from another function. It involves subtracting the corresponding terms of the two functions and combining like terms to simplify the expression.

Q2: How do I perform function subtraction?

A2: To perform function subtraction, you need to subtract the corresponding terms of the two functions. For example, if you have two functions, f(x) and g(x), you need to subtract g(x) from f(x) to get (f-g)(x).

Q3: What is the difference between function subtraction and function addition?

A3: Function subtraction and function addition are two different operations. Function subtraction involves subtracting one function from another, while function addition involves adding one function to another.

Q4: How do I simplify an expression after performing function subtraction?

A4: To simplify an expression after performing function subtraction, you need to combine like terms. This involves adding or subtracting the coefficients of the same variables.

Q5: What are some common mistakes to avoid when performing function subtraction?

A5: Some common mistakes to avoid when performing function subtraction include forgetting to subtract the corresponding terms of the two functions and combining like terms incorrectly.

Q6: How do I check my answer after performing function subtraction?

A6: To check your answer after performing function subtraction, you need to compare it with the answer choices. Make sure to check the answer choices carefully and select the correct one.

Q7: What are some real-world applications of function subtraction?

A7: Function subtraction has many real-world applications, such as in physics and engineering. For example, when calculating the difference between two physical quantities, such as velocity and acceleration, we need to subtract the corresponding terms of the two quantities.

Q8: Can I use function subtraction to find the difference between two functions that are not in the same form?

A8: Yes, you can use function subtraction to find the difference between two functions that are not in the same form. However, you need to make sure that the functions are in a form that allows you to subtract them.

Q9: How do I handle functions with different variables when performing function subtraction?

A9: When performing function subtraction, you need to make sure that the functions have the same variable. If the functions have different variables, you need to substitute the variables to make them the same.

Q10: Can I use function subtraction to find the difference between two functions that are not defined for the same domain?

A10: No, you cannot use function subtraction to find the difference between two functions that are not defined for the same domain. Function subtraction requires that the functions are defined for the same domain.

Conclusion

In conclusion, function subtraction is an important concept in mathematics that requires us to understand how to subtract the corresponding terms of two functions and combine like terms to simplify the expression. By following the steps outlined in this article, you can perform function subtraction and check your answer to ensure that you get the correct result.

Related Articles

• Function Addition
• Function Composition
• Function Inverse

Tips and Tricks

• Make sure to subtract the corresponding terms of the two functions when performing function subtraction.
• Combine like terms carefully to simplify the expression.
• Check the answer choices carefully to select the correct one.

Common Mistakes

• Forgetting to subtract the corresponding terms of the two functions.
• Combining like terms incorrectly.
• Not checking the answer choices carefully.

Real-World Applications

• Physics: Function subtraction is used to calculate the difference between two physical quantities, such as velocity and acceleration.
• Engineering: Function subtraction is used to calculate the difference between two engineering quantities, such as force and displacement.

Conclusion

In conclusion, function subtraction is an important concept in mathematics that requires us to understand how to subtract the corresponding terms of two functions and combine like terms to simplify the expression. By following the steps outlined in this article, you can perform function subtraction and check your answer to ensure that you get the correct result.