If $f(x)=3^x+10x$ And $g(x)=2x-4$, Find $(f-g)(x$\].A. $3^x+12x-4$ B. $15x-4$ C. $3^x-8x+4$ D. $3^x+8x+4$

$$$$$$

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: $f(x)=3^x+10x$ and $g(x)=2x-4$. We need to find the difference between these two functions, which is denoted as $(f-g)(x)$.

Subtracting the Functions

To find the difference between the two functions, we need to subtract the second function from the first function. This means we need to subtract $g(x)$ from $f(x)$. We can do this by subtracting the corresponding terms of the two functions.

Step 1: Subtract the Constant Terms

The first step is to subtract the constant terms of the two functions. In this case, the constant term of $f(x)$ is 0, and the constant term of $g(x)$ is -4. Therefore, the difference between the constant terms is:

$$0 - (-4) = 4$$

Step 2: Subtract the Variable Terms

The next step is to subtract the variable terms of the two functions. In this case, the variable term of $f(x)$ is $3^x$, and the variable term of $g(x)$ is $2x$. Therefore, the difference between the variable terms is:

$$3^x - 2x$$

Step 3: Combine the Results

Now that we have subtracted the constant terms and the variable terms, we can combine the results to find the difference between the two functions. Therefore, the difference between the two functions is:

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

Simplifying the Result

We can simplify the result by combining the like terms. In this case, we can combine the $-2x$ term with the $+4$ term to get:

$$(f-g)(x) = 3^x - 2x + 4 = 3^x - 8x + 4$$

Conclusion

Therefore, the difference between the two functions is $(f-g)(x) = 3^x - 8x + 4$.

Answer

The correct answer is C. $3^x-8x+4$.

Discussion

This problem requires us to understand the concept of subtracting functions. We need to subtract the second function from the first function, which involves subtracting the corresponding terms of the two functions. This problem also requires us to simplify the result by combining like terms.

Example

Let's consider an example to illustrate this concept. Suppose we have two functions: $f(x) = 2x + 3$ and $g(x) = x - 2$. We need to find the difference between these two functions, which is denoted as $(f-g)(x)$.

To find the difference between the two functions, we need to subtract the second function from the first function. This means we need to subtract $g(x)$ from $f(x)$. We can do this by subtracting the corresponding terms of the two functions.

The first step is to subtract the constant terms of the two functions. In this case, the constant term of $f(x)$ is 3, and the constant term of $g(x)$ is -2. Therefore, the difference between the constant terms is:

$$3 - (-2) = 5$$

The next step is to subtract the variable terms of the two functions. In this case, the variable term of $f(x)$ is $2x$, and the variable term of $g(x)$ is $x$. Therefore, the difference between the variable terms is:

$$2x - x = x$$

Now that we have subtracted the constant terms and the variable terms, we can combine the results to find the difference between the two functions. Therefore, the difference between the two functions is:

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

This example illustrates the concept of subtracting functions. We need to subtract the second function from the first function, which involves subtracting the corresponding terms of the two functions.

Applications

This concept of subtracting functions has many applications in mathematics and other fields. For example, it is used in calculus to find the difference between two functions, and it is also used in physics to find the difference between two physical quantities.

Conclusion

In conclusion, the difference between two functions is found by subtracting the second function from the first function. This involves subtracting the corresponding terms of the two functions and simplifying the result by combining like terms. This concept has many applications in mathematics and other fields.

References

• [1] "Functions" by Khan Academy
• [2] "Subtracting Functions" by Math Open Reference
• [3] "Calculus" by MIT OpenCourseWare

Keywords

• Functions
• Subtracting functions
• Difference between functions
• Calculus
• Physics

Related Topics

• Adding functions
• Multiplying functions
• Dividing functions
• Composition of functions

Further Reading

• "Functions" by Khan Academy
• "Calculus" by MIT OpenCourseWare
• "Physics" by OpenStax

FAQs

• Q: What is the difference between two functions? A: The difference between two functions is found by subtracting the second function from the first function.
• Q: How do I subtract two functions? A: To subtract two functions, you need to subtract the corresponding terms of the two functions and simplify the result by combining like terms.
• Q: What are the applications of subtracting functions? A: The concept of subtracting functions has many applications in mathematics and other fields, including calculus and physics.
  

Understanding the Concept

Subtracting functions is a fundamental concept in mathematics that involves finding the difference between two functions. In this article, we will answer some of the most frequently asked questions about subtracting functions.

Q: What is the difference between two functions?

A: The difference between two functions is found by subtracting the second function from the first function. This involves subtracting the corresponding terms of the two functions and simplifying the result by combining like terms.

Q: How do I subtract two functions?

A: To subtract two functions, you need to follow these steps:

1. Identify the two functions that you want to subtract.
2. Subtract the corresponding terms of the two functions.
3. Simplify the result by combining like terms.

Q: What are the rules for subtracting functions?

A: The rules for subtracting functions are as follows:

1. Subtract the constant terms of the two functions.
2. Subtract the variable terms of the two functions.
3. Simplify the result by combining like terms.

Q: Can I subtract a function from a constant?

A: No, you cannot subtract a function from a constant. The result of subtracting a function from a constant is undefined.

Q: Can I subtract a constant from a function?

A: Yes, you can subtract a constant from a function. This involves subtracting the constant term from the function.

Q: What are the applications of subtracting functions?

A: The concept of subtracting functions has many applications in mathematics and other fields, including calculus and physics.

Q: How do I use subtracting functions in real-life situations?

A: Subtracting functions is used in many real-life situations, such as:

1. Finding the difference between two physical quantities.
2. Calculating the rate of change of a function.
3. Finding the maximum or minimum value of a function.

Q: What are some common mistakes to avoid when subtracting functions?

A: Some common mistakes to avoid when subtracting functions include:

1. Not simplifying the result by combining like terms.
2. Not following the order of operations.
3. Not checking for undefined results.

Q: How do I check my work when subtracting functions?

A: To check your work when subtracting functions, you can:

1. Plug in a value for the variable and check if the result is correct.
2. Use a calculator to check if the result is correct.
3. Check if the result is a function.

Q: What are some tips for mastering subtracting functions?

A: Some tips for mastering subtracting functions include:

1. Practice, practice, practice.
2. Start with simple functions and work your way up to more complex functions.
3. Use visual aids, such as graphs and charts, to help you understand the concept.

Q: How do I use technology to help me with subtracting functions?

A: There are many online tools and resources available to help you with subtracting functions, including:

1. Graphing calculators.
2. Online function calculators.
3. Math software.

Q: What are some common errors to watch out for when subtracting functions?

A: Some common errors to watch out for when subtracting functions include:

1. Not following the order of operations.
2. Not simplifying the result by combining like terms.
3. Not checking for undefined results.

Q: How do I use subtracting functions in algebra?

A: Subtracting functions is used in algebra to find the difference between two polynomials.

Q: What are some real-world applications of subtracting functions in algebra?

A: Some real-world applications of subtracting functions in algebra include:

1. Finding the difference between two polynomial expressions.
2. Calculating the rate of change of a polynomial function.
3. Finding the maximum or minimum value of a polynomial function.

Q: How do I use subtracting functions in calculus?

A: Subtracting functions is used in calculus to find the difference between two functions.

Q: What are some real-world applications of subtracting functions in calculus?

A: Some real-world applications of subtracting functions in calculus include:

1. Finding the difference between two functions.
2. Calculating the rate of change of a function.
3. Finding the maximum or minimum value of a function.

Q: How do I use subtracting functions in physics?

A: Subtracting functions is used in physics to find the difference between two physical quantities.

Q: What are some real-world applications of subtracting functions in physics?

A: Some real-world applications of subtracting functions in physics include:

1. Finding the difference between two physical quantities.
2. Calculating the rate of change of a physical quantity.
3. Finding the maximum or minimum value of a physical quantity.

Conclusion

In conclusion, subtracting functions is a fundamental concept in mathematics that involves finding the difference between two functions. By understanding the rules and applications of subtracting functions, you can use this concept to solve a wide range of problems in mathematics and other fields.