For F ( X ) = 4 X + 1 F(x)=4x+1 F ( X ) = 4 X + 1 And G ( X ) = X 2 − 5 G(x)=x^2-5 G ( X ) = X 2 − 5 , Find ( F ⋅ G ) ( X (f \cdot G)(x ( F ⋅ G ) ( X ].A. 4 X 3 + X 2 − 4 X − 6 4x^3 + X^2 - 4x - 6 4 X 3 + X 2 − 4 X − 6 B. 4 X 2 − 19 4x^2 - 19 4 X 2 − 19 C. 4 X 3 + X 2 − 20 X − 5 4x^3 + X^2 - 20x - 5 4 X 3 + X 2 − 20 X − 5 D. 4 X 3 + X 2 − 5 X − 5 4x^3 + X^2 - 5x - 5 4 X 3 + X 2 − 5 X − 5

Introduction

In mathematics, functions are used to describe the relationship between variables. When we multiply two functions, we need to follow a specific procedure to obtain the resulting function. In this article, we will explore how to multiply two functions, using the given functions $f(x)=4x+1$ and $g(x)=x^2-5$ as examples.

Understanding Function Multiplication

When we multiply two functions, we need to multiply each term of the first function by each term of the second function. This means that we will have multiple terms in the resulting function, each of which is the product of a term from the first function and a term from the second function.

Step 1: Multiply Each Term of the First Function by Each Term of the Second Function

To multiply the functions $f(x)=4x+1$ and $g(x)=x^2-5$, we need to multiply each term of the first function by each term of the second function.

• Multiply the first term of the first function ($4x$) by each term of the second function ($x^2$ and $-5$):
  • $4x \cdot x^2 = 4x^3$
  • $4x \cdot (-5) = -20x$
• Multiply the second term of the first function ($1$) by each term of the second function ($x^2$ and $-5$):
  • $1 \cdot x^2 = x^2$
  • $1 \cdot (-5) = -5$

Step 2: Combine Like Terms

Now that we have multiplied each term of the first function by each term of the second function, we need to combine like terms. Like terms are terms that have the same variable(s) raised to the same power.

• Combine the terms $4x^3$ and $0$ (since there is no other term with $x^3$):
  • $4x^3 + 0 = 4x^3$
• Combine the terms $-20x$ and $0$ (since there is no other term with $x$):
  • $-20x + 0 = -20x$
• Combine the terms $x^2$ and $-5$:
  • $x^2 - 5$

Step 3: Write the Resulting Function

Now that we have combined like terms, we can write the resulting function.

$(f \cdot g)(x) = 4x^3 - 20x + x^2 - 5$

Simplifying the Resulting Function

We can simplify the resulting function by combining like terms.

$(f \cdot g)(x) = 4x^3 + x^2 - 20x - 5$

Conclusion

In this article, we have explored how to multiply two functions, using the given functions $f(x)=4x+1$ and $g(x)=x^2-5$ as examples. We have followed a step-by-step procedure to obtain the resulting function, and we have simplified the resulting function by combining like terms. The resulting function is $(f \cdot g)(x) = 4x^3 + x^2 - 20x - 5$.

Answer

The correct answer is:

Introduction

In our previous article, we explored how to multiply two functions, using the given functions $f(x)=4x+1$ and $g(x)=x^2-5$ as examples. In this article, we will answer some frequently asked questions about multiplying two functions.

Q: What is the order of operations when multiplying two functions?

A: When multiplying two functions, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate any expressions inside parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

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

A: When multiplying two functions with different variables, we need to multiply each term of the first function by each term of the second function. For example, if we have the functions $f(x)=4x+1$ and $g(y)=y^2-5$, we need to multiply each term of the first function by each term of the second function.

• Multiply the first term of the first function ($4x$) by each term of the second function ($y^2$ and $-5$):
  • $4x \cdot y^2 = 4xy^2$
  • $4x \cdot (-5) = -20x$
• Multiply the second term of the first function ($1$) by each term of the second function ($y^2$ and $-5$):
  • $1 \cdot y^2 = y^2$
  • $1 \cdot (-5) = -5$

Q: How do I multiply two functions with the same variable?

A: When multiplying two functions with the same variable, we need to multiply each term of the first function by each term of the second function. For example, if we have the functions $f(x)=4x+1$ and $g(x)=x^2-5$, we need to multiply each term of the first function by each term of the second function.

• Multiply the first term of the first function ($4x$) by each term of the second function ($x^2$ and $-5$):
  • $4x \cdot x^2 = 4x^3$
  • $4x \cdot (-5) = -20x$
• Multiply the second term of the first function ($1$) by each term of the second function ($x^2$ and $-5$):
  • $1 \cdot x^2 = x^2$
  • $1 \cdot (-5) = -5$

Q: Can I simplify the resulting function after multiplying two functions?

A: Yes, you can simplify the resulting function after multiplying two functions. To simplify the resulting function, you need to combine like terms. Like terms are terms that have the same variable(s) raised to the same power.

Q: What is the difference between multiplying two functions and adding two functions?

A: Multiplying two functions involves multiplying each term of the first function by each term of the second function, whereas adding two functions involves adding the corresponding terms of the two functions.

Conclusion

In this article, we have answered some frequently asked questions about multiplying two functions. We have covered topics such as the order of operations, multiplying functions with different variables, multiplying functions with the same variable, simplifying the resulting function, and the difference between multiplying and adding two functions.

Answer

The correct answers are:

• Q: What is the order of operations when multiplying two functions? A: The order of operations is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
• Q: How do I multiply two functions with different variables? A: Multiply each term of the first function by each term of the second function.
• Q: How do I multiply two functions with the same variable? A: Multiply each term of the first function by each term of the second function.
• Q: Can I simplify the resulting function after multiplying two functions? A: Yes, you can simplify the resulting function by combining like terms.
• Q: What is the difference between multiplying two functions and adding two functions? A: Multiplying two functions involves multiplying each term of the first function by each term of the second function, whereas adding two functions involves adding the corresponding terms of the two functions.