Use F ( X ) = 3 X F(x)=3x F ( X ) = 3 X And G ( X ) = X + 2 G(x)=x+2 G ( X ) = X + 2 To Evaluate Each Of The Following:(a) { (f+g)(5)$}$(b) { (f-g)(2)$}$(c) { (fg)(1)$}$(d) { (f/g)(0)$}$A. { (f-g)(2)= \square$}$ (Type A Whole Number.)B.

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Introduction

In mathematics, functions play a crucial role in representing relationships between variables. Two functions, $f(x)$ and $g(x)$, are given as $f(x)=3x$ and $g(x)=x+2$. These functions can be combined in various ways to form new functions, such as the sum, difference, product, and quotient. In this article, we will explore how to evaluate each of these combinations using the given functions.

Evaluating the Sum of $f(x)$ and $g(x)$

The sum of two functions, $f(x)$ and $g(x)$, is denoted as $(f+g)(x)$. To evaluate this combination, we need to add the corresponding terms of $f(x)$ and $g(x)$. In this case, we have:

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

Simplifying the expression, we get:

$(f+g)(x) = 4x + 2$

Now, we can evaluate the sum of $f(x)$ and $g(x)$ at $x=5$:

$(f+g)(5) = 4(5) + 2 = 20 + 2 = 22$

Evaluating the Difference of $f(x)$ and $g(x)$

The difference of two functions, $f(x)$ and $g(x)$, is denoted as $(f-g)(x)$. To evaluate this combination, we need to subtract the corresponding terms of $g(x)$ from $f(x)$. In this case, we have:

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

Simplifying the expression, we get:

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

Now, we can evaluate the difference of $f(x)$ and $g(x)$ at $x=2$:

$(f-g)(2) = 2(2) - 2 = 4 - 2 = 2$

Evaluating the Product of $f(x)$ and $g(x)$

The product of two functions, $f(x)$ and $g(x)$, is denoted as $(fg)(x)$. To evaluate this combination, we need to multiply the corresponding terms of $f(x)$ and $g(x)$. In this case, we have:

$(fg)(x) = f(x) \cdot g(x) = 3x \cdot (x+2)$

Expanding the expression, we get:

$(fg)(x) = 3x^2 + 6x$

Now, we can evaluate the product of $f(x)$ and $g(x)$ at $x=1$:

$(fg)(1) = 3(1)^2 + 6(1) = 3 + 6 = 9$

Evaluating the Quotient of $f(x)$ and $g(x)$

The quotient of two functions, $f(x)$ and $g(x)$, is denoted as $(f/g)(x)$. To evaluate this combination, we need to divide the corresponding terms of $f(x)$ by $g(x)$. In this case, we have:

$(f/g)(x) = \frac{f(x)}{g(x)} = \frac{3x}{x+2}$

Now, we can evaluate the quotient of $f(x)$ and $g(x)$ at $x=0$:

$(f/g)(0) = \frac{3(0)}{0+2} = \frac{0}{2} = 0$

Conclusion

In this article, we have evaluated the sum, difference, product, and quotient of two functions, $f(x)$ and $g(x)$. We have used the given functions $f(x)=3x$ and $g(x)=x+2$ to find the values of each combination at specific points. These evaluations demonstrate the importance of understanding function combinations and how they can be used to solve mathematical problems.

Discussion

The evaluation of function combinations is a fundamental concept in mathematics, and it has numerous applications in various fields, such as physics, engineering, and economics. By understanding how to evaluate the sum, difference, product, and quotient of functions, we can solve a wide range of mathematical problems and make informed decisions in real-world scenarios.

Final Thoughts

In conclusion, the evaluation of function combinations is a crucial aspect of mathematics that requires a deep understanding of function notation and algebraic manipulation. By mastering these concepts, we can tackle complex mathematical problems and make meaningful contributions to various fields of study.

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Introduction

In our previous article, we explored how to evaluate the sum, difference, product, and quotient of two functions, $f(x)$ and $g(x)$. We used the given functions $f(x)=3x$ and $g(x)=x+2$ to find the values of each combination at specific points. In this article, we will address some common questions and provide additional insights to help you better understand function combinations.

Q&A

Q: What is the difference between the sum and difference of two functions?

A: The sum of two functions, $(f+g)(x)$, is the result of adding the corresponding terms of $f(x)$ and $g(x)$. On the other hand, the difference of two functions, $(f-g)(x)$, is the result of subtracting the corresponding terms of $g(x)$ from $f(x)$.

Q: How do I evaluate the product of two functions?

A: To evaluate the product of two functions, $(fg)(x)$, you need to multiply the corresponding terms of $f(x)$ and $g(x)$. For example, if $f(x)=3x$ and $g(x)=x+2$, then $(fg)(x) = 3x \cdot (x+2) = 3x^2 + 6x$.

Q: What is the quotient of two functions?

A: The quotient of two functions, $(f/g)(x)$, is the result of dividing the corresponding terms of $f(x)$ by $g(x)$. For example, if $f(x)=3x$ and $g(x)=x+2$, then $(f/g)(x) = \frac{3x}{x+2}$.

Q: Can I evaluate the sum, difference, product, and quotient of functions with different variables?

A: Yes, you can evaluate the sum, difference, product, and quotient of functions with different variables. However, you need to make sure that the variables are defined and that the functions are well-defined at the point of evaluation.

Q: How do I handle undefined values when evaluating function combinations?

A: When evaluating function combinations, you may encounter undefined values, such as division by zero. In such cases, you need to carefully analyze the situation and determine whether the function is well-defined at the point of evaluation.

Q: Can I use function combinations to solve real-world problems?

A: Yes, function combinations can be used to solve a wide range of real-world problems. For example, in physics, you can use function combinations to model the motion of objects, while in economics, you can use function combinations to model the behavior of economic systems.

Conclusion

In this article, we have addressed some common questions and provided additional insights to help you better understand function combinations. By mastering the concepts of function combinations, you can tackle complex mathematical problems and make meaningful contributions to various fields of study.

Final Thoughts

In conclusion, function combinations are a powerful tool for solving mathematical problems and modeling real-world phenomena. By understanding how to evaluate the sum, difference, product, and quotient of functions, you can unlock new possibilities and make a meaningful impact in your field of study.

Additional Resources

• Function Notation
• Algebraic Manipulation
• Function Combinations

Discussion

The evaluation of function combinations is a fundamental concept in mathematics that has numerous applications in various fields. By understanding how to evaluate the sum, difference, product, and quotient of functions, you can solve complex mathematical problems and make meaningful contributions to your field of study.

Final Q&A

Do you have any additional questions about function combinations? Please feel free to ask, and we will do our best to provide a helpful response.