Subtract The Following Functions:$\[ \begin{array}{l} f(x) = -5x^2 + X - 2 \\ g(x) = -3x^2 + 3x + 9 \end{array} \\]Choose The Correct Result:A. \[$2x^2 + 2x - 11\$\]B. \[$-2x^2 - 2x - 11\$\]C. \[$2x^2 - 2x + 11\$\]D.

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Introduction

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In mathematics, functions are used to describe relationships between variables. When we have two functions, we can perform various operations on them, including addition and subtraction. In this article, we will focus on subtracting functions, specifically the functions $f(x) = -5x^2 + x - 2$ and $g(x) = -3x^2 + 3x + 9$. We will walk through the step-by-step process of subtracting these functions and provide the correct result.

Understanding Functions

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Before we proceed with subtracting functions, let's briefly review what functions are. A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). In mathematical notation, a function is often represented as $f(x)$, where $x$ is the input and $f(x)$ is the output.

Subtracting Functions

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To subtract two functions, we need to follow the same rules as subtracting polynomials. We will subtract the corresponding terms of the two functions.

Step 1: Write Down the Functions

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Let's write down the two functions we want to subtract:

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

$g(x) = -3x^2 + 3x + 9$

Step 2: Subtract the Corresponding Terms

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Now, let's subtract the corresponding terms of the two functions:

$f(x) - g(x) = (-5x^2 + x - 2) - (-3x^2 + 3x + 9)$

To subtract the terms, we need to change the sign of the terms in the second function:

$f(x) - g(x) = (-5x^2 + x - 2) + (3x^2 - 3x - 9)$

Step 3: Combine Like Terms

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Now, let's combine the like terms:

$f(x) - g(x) = (-5x^2 + 3x^2) + (x - 3x) + (-2 - 9)$

Combine the like terms:

$f(x) - g(x) = -2x^2 - 2x - 11$

Conclusion

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In conclusion, when we subtract the functions $f(x) = -5x^2 + x - 2$ and $g(x) = -3x^2 + 3x + 9$, we get the result $f(x) - g(x) = -2x^2 - 2x - 11$. This is the correct result.

Discussion

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The correct result is option B: $-2x^2 - 2x - 11$. This is the result we obtained by following the step-by-step process of subtracting functions.

Final Answer

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The final answer is option B: $-2x^2 - 2x - 11$.

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Introduction

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In our previous article, we discussed how to subtract functions, specifically the functions $f(x) = -5x^2 + x - 2$ and $g(x) = -3x^2 + 3x + 9$. We walked through the step-by-step process of subtracting these functions and provided the correct result. In this article, we will answer some frequently asked questions related to subtracting functions.

Q&A

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Q: What is the difference between subtracting functions and subtracting polynomials?

A: Subtracting functions and subtracting polynomials are similar operations. When we subtract two functions, we are essentially subtracting two polynomials. The rules for subtracting polynomials apply to subtracting functions as well.

Q: How do I subtract two functions with different variables?

A: When subtracting two functions with different variables, we need to use the distributive property to expand the functions. For example, if we want to subtract the functions $f(x) = -5x^2 + x - 2$ and $g(y) = -3y^2 + 3y + 9$, we need to expand the functions using the distributive property.

Q: Can I subtract a function from itself?

A: Yes, you can subtract a function from itself. When we subtract a function from itself, we get the result $0$. For example, if we want to subtract the function $f(x) = -5x^2 + x - 2$ from itself, we get the result $f(x) - f(x) = 0$.

Q: How do I subtract a constant from a function?

A: When subtracting a constant from a function, we need to subtract the constant from each term of the function. For example, if we want to subtract the constant $5$ from the function $f(x) = -5x^2 + x - 2$, we get the result $f(x) - 5 = -5x^2 + x - 7$.

Q: Can I subtract a function from a polynomial?

A: Yes, you can subtract a function from a polynomial. When we subtract a function from a polynomial, we need to follow the rules for subtracting polynomials. For example, if we want to subtract the function $f(x) = -5x^2 + x - 2$ from the polynomial $p(x) = 3x^2 + 2x + 1$, we get the result $p(x) - f(x) = 8x^2 + 3x + 3$.

Conclusion

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In conclusion, subtracting functions is a fundamental operation in mathematics that can be used to solve a wide range of problems. By following the rules for subtracting polynomials and using the distributive property, we can subtract functions with different variables and constants. We hope this article has provided you with a better understanding of subtracting functions and has answered some of the frequently asked questions related to this topic.

Final Answer

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The final answer is that subtracting functions is a powerful tool that can be used to solve a wide range of problems in mathematics. By following the rules for subtracting polynomials and using the distributive property, we can subtract functions with different variables and constants.