If $f(x)=2x^2-3x+2$ And $g(x)=2x^2-3x-2$, What Is $f(x)-g(x$\]?A. $6x+4$ B. 0 C. $4x^2-6x$ D. 4

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Understanding the Problem

To find the value of $f(x)-g(x)$, we need to understand the concept of subtraction in algebra. When we subtract two functions, we are essentially finding the difference between their respective outputs for a given input. In this case, we are given two quadratic functions, $f(x)$ and $g(x)$, and we need to find their difference.

Subtraction of Functions

The subtraction of functions is a straightforward process. We simply subtract the corresponding terms of the two functions. In this case, we have:

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

$g(x) = 2x^2 - 3x - 2$

To find $f(x) - g(x)$, we subtract the corresponding terms:

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

Simplifying the Expression

Now, let's simplify the expression by combining like terms. We can start by removing the parentheses and combining the like terms:

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

Combining Like Terms

Next, we can combine the like terms. The $2x^2$ terms cancel each other out, and the $-3x$ and $+3x$ terms also cancel each other out. We are left with:

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

Evaluating the Expression

Finally, we can evaluate the expression by adding the two constants:

$f(x) - g(x) = 4$

Conclusion

In conclusion, the value of $f(x)-g(x)$ is $4$. This means that when we subtract the function $g(x)$ from the function $f(x)$, we get a constant value of $4$.

Example Use Case

This concept of subtracting functions is useful in many real-world applications, such as:

• Finding the difference between two population growth rates
• Calculating the difference between two investment returns
• Determining the difference between two physical quantities, such as temperature or pressure

Step-by-Step Solution

Here is a step-by-step solution to the problem:

1. Write down the two functions: $f(x) = 2x^2 - 3x + 2$ and $g(x) = 2x^2 - 3x - 2$
2. Subtract the corresponding terms: $f(x) - g(x) = (2x^2 - 3x + 2) - (2x^2 - 3x - 2)$
3. Simplify the expression by combining like terms: $f(x) - g(x) = 2x^2 - 3x + 2 - 2x^2 + 3x + 2$
4. Combine the like terms: $f(x) - g(x) = 2 + 2$
5. Evaluate the expression: $f(x) - g(x) = 4$

Final Answer

The final answer is $\boxed{4}$.

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Understanding the Problem

To find the value of $f(x)-g(x)$, we need to understand the concept of subtraction in algebra. When we subtract two functions, we are essentially finding the difference between their respective outputs for a given input. In this case, we are given two quadratic functions, $f(x)$ and $g(x)$, and we need to find their difference.

Q&A Session

Q: What is the difference between $f(x)$ and $g(x)$?

A: The difference between $f(x)$ and $g(x)$ is the value of $f(x)-g(x)$.

Q: How do we find the value of $f(x)-g(x)$?

A: To find the value of $f(x)-g(x)$, we need to subtract the corresponding terms of the two functions.

Q: What are the corresponding terms of the two functions?

A: The corresponding terms of the two functions are the terms with the same variable and exponent.

Q: How do we simplify the expression?

A: We simplify the expression by combining like terms.

Q: What are like terms?

A: Like terms are terms with the same variable and exponent.

Q: How do we combine like terms?

A: We combine like terms by adding or subtracting their coefficients.

Q: What is the final answer?

A: The final answer is $\boxed{4}$.

Example Questions and Answers

Q: If $f(x)=x^2+2x+1$ and $g(x)=x^2+2x-1$, what is $f(x)-g(x)$?

A: To find the value of $f(x)-g(x)$, we need to subtract the corresponding terms of the two functions.

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

Simplifying the expression, we get:

$f(x)-g(x) = 2$

Q: If $f(x)=3x^2-2x+1$ and $g(x)=3x^2-2x-1$, what is $f(x)-g(x)$?

A: To find the value of $f(x)-g(x)$, we need to subtract the corresponding terms of the two functions.

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

Simplifying the expression, we get:

$f(x)-g(x) = 2$

Q: If $f(x)=2x^2-3x+2$ and $g(x)=2x^2-3x-2$, what is $f(x)-g(x)$?

A: To find the value of $f(x)-g(x)$, we need to subtract the corresponding terms of the two functions.

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

Simplifying the expression, we get:

$f(x)-g(x) = 4$

Conclusion

In conclusion, the value of $f(x)-g(x)$ is $4$. This means that when we subtract the function $g(x)$ from the function $f(x)$, we get a constant value of $4$.

Step-by-Step Solution

Here is a step-by-step solution to the problem:

1. Write down the two functions: $f(x) = 2x^2 - 3x + 2$ and $g(x) = 2x^2 - 3x - 2$
2. Subtract the corresponding terms: $f(x) - g(x) = (2x^2 - 3x + 2) - (2x^2 - 3x - 2)$
3. Simplify the expression by combining like terms: $f(x) - g(x) = 2x^2 - 3x + 2 - 2x^2 + 3x + 2$
4. Combine the like terms: $f(x) - g(x) = 2 + 2$
5. Evaluate the expression: $f(x) - g(x) = 4$

Final Answer

The final answer is $\boxed{4}$.