Evaluate The Function Operations Using The Given Functions And The Given Value Of { X$}$.Given: ${ F(x) = -3x }$ { G(x) = |x+2| \} ${ H(x) = \frac{1}{x-1} }$37. { (f + H)(2)$} 38. \[ 38. \[ 38. \[ (g \cdot

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Introduction

In mathematics, function operations are a crucial concept that deals with combining two or more functions to create a new function. This can be done using various operations such as addition, subtraction, multiplication, and division. In this article, we will evaluate the function operations using the given functions and the given value of $x$. We will use the functions $f(x) = -3x$, $g(x) = |x+2|$, and $h(x) = \frac{1}{x-1}$ to perform the operations.

Evaluating $(f + h)(2)$

To evaluate $(f + h)(2)$, we need to first find the values of $f(2)$ and $h(2)$.

Finding $f(2)$

We are given that $f(x) = -3x$. To find $f(2)$, we substitute $x = 2$ into the function.

$f(2) = -3(2) = -6$

Finding $h(2)$

We are given that $h(x) = \frac{1}{x-1}$. To find $h(2)$, we substitute $x = 2$ into the function.

$h(2) = \frac{1}{2-1} = \frac{1}{1} = 1$

Evaluating $(f + h)(2)$

Now that we have found the values of $f(2)$ and $h(2)$, we can evaluate $(f + h)(2)$.

$(f + h)(2) = f(2) + h(2) = -6 + 1 = -5$

Evaluating $(g \cdot h)(2)$

To evaluate $(g \cdot h)(2)$, we need to first find the values of $g(2)$ and $h(2)$.

Finding $g(2)$

We are given that $g(x) = |x+2|$. To find $g(2)$, we substitute $x = 2$ into the function.

$g(2) = |2+2| = |4| = 4$

Finding $h(2)$

We have already found the value of $h(2)$ in the previous section.

$h(2) = 1$

Evaluating $(g \cdot h)(2)$

Now that we have found the values of $g(2)$ and $h(2)$, we can evaluate $(g \cdot h)(2)$.

$(g \cdot h)(2) = g(2) \cdot h(2) = 4 \cdot 1 = 4$

Evaluating $(f \cdot g)(2)$

To evaluate $(f \cdot g)(2)$, we need to first find the values of $f(2)$ and $g(2)$.

Finding $f(2)$

We have already found the value of $f(2)$ in the previous section.

$f(2) = -6$

Finding $g(2)$

We have already found the value of $g(2)$ in the previous section.

$g(2) = 4$

Evaluating $(f \cdot g)(2)$

Now that we have found the values of $f(2)$ and $g(2)$, we can evaluate $(f \cdot g)(2)$.

$(f \cdot g)(2) = f(2) \cdot g(2) = -6 \cdot 4 = -24$

Evaluating $(f - g)(2)$

To evaluate $(f - g)(2)$, we need to first find the values of $f(2)$ and $g(2)$.

Finding $f(2)$

We have already found the value of $f(2)$ in the previous section.

$f(2) = -6$

Finding $g(2)$

We have already found the value of $g(2)$ in the previous section.

$g(2) = 4$

Evaluating $(f - g)(2)$

Now that we have found the values of $f(2)$ and $g(2)$, we can evaluate $(f - g)(2)$.

$(f - g)(2) = f(2) - g(2) = -6 - 4 = -10$

Evaluating $(f / g)(2)$

To evaluate $(f / g)(2)$, we need to first find the values of $f(2)$ and $g(2)$.

Finding $f(2)$

We have already found the value of $f(2)$ in the previous section.

$f(2) = -6$

Finding $g(2)$

We have already found the value of $g(2)$ in the previous section.

$g(2) = 4$

Evaluating $(f / g)(2)$

Now that we have found the values of $f(2)$ and $g(2)$, we can evaluate $(f / g)(2)$.

$(f / g)(2) = f(2) / g(2) = -6 / 4 = -\frac{3}{2}$

Conclusion

In this article, we evaluated the function operations using the given functions and the given value of $x$. We used the functions $f(x) = -3x$, $g(x) = |x+2|$, and $h(x) = \frac{1}{x-1}$ to perform the operations. We found the values of $(f + h)(2)$, $(g \cdot h)(2)$, $(f \cdot g)(2)$, $(f - g)(2)$, and $(f / g)(2)$. The results are as follows:

• $(f + h)(2) = -5$
• $(g \cdot h)(2) = 4$
• $(f \cdot g)(2) = -24$
• $(f - g)(2) = -10$
• $(f / g)(2) = -\frac{3}{2}$

These results demonstrate the importance of function operations in mathematics and how they can be used to create new functions.

Introduction

In our previous article, we evaluated the function operations using the given functions and the given value of $x$. We used the functions $f(x) = -3x$, $g(x) = |x+2|$, and $h(x) = \frac{1}{x-1}$ to perform the operations. In this article, we will answer some frequently asked questions related to function operations.

Q1: What is the difference between function addition and function multiplication?

A1: Function addition and function multiplication are two different operations that can be performed on functions. Function addition involves adding two or more functions together, while function multiplication involves multiplying two or more functions together.

Q2: How do I evaluate a function operation with multiple functions?

A2: To evaluate a function operation with multiple functions, you need to follow the order of operations (PEMDAS). First, evaluate the expressions inside the parentheses, then evaluate any exponential expressions, followed by any multiplication and division operations, and finally any addition and subtraction operations.

Q3: What is the value of $(f \cdot g)(x)$ when $f(x) = 2x$ and $g(x) = x^2$?

A3: To evaluate $(f \cdot g)(x)$, we need to multiply the two functions together. $(f \cdot g)(x) = f(x) \cdot g(x) = 2x \cdot x^2 = 2x^3$

Q4: How do I evaluate a function operation with a constant?

A4: To evaluate a function operation with a constant, you can treat the constant as a function that always returns the same value. For example, if we have the function $f(x) = 2x$ and we want to evaluate $(f + 3)(x)$, we can treat the constant 3 as a function that always returns 3. $(f + 3)(x) = f(x) + 3 = 2x + 3$

Q5: What is the value of $(f / g)(x)$ when $f(x) = x^2$ and $g(x) = x$?

A5: To evaluate $(f / g)(x)$, we need to divide the two functions together. $(f / g)(x) = f(x) / g(x) = x^2 / x = x$

Q6: How do I evaluate a function operation with a rational function?

A6: To evaluate a function operation with a rational function, you can follow the same steps as evaluating a function operation with a polynomial function. For example, if we have the function $f(x) = x^2$ and we want to evaluate $(f / (x + 1))(x)$, we can treat the rational function $x + 1$ as a function that always returns the value of $x + 1$. $(f / (x + 1))(x) = f(x) / (x + 1) = x^2 / (x + 1)$

Q7: What is the value of $(f - g)(x)$ when $f(x) = 2x$ and $g(x) = x^2$?

A7: To evaluate $(f - g)(x)$, we need to subtract the two functions together. $(f - g)(x) = f(x) - g(x) = 2x - x^2$

Q8: How do I evaluate a function operation with a trigonometric function?

A8: To evaluate a function operation with a trigonometric function, you can follow the same steps as evaluating a function operation with a polynomial function. For example, if we have the function $f(x) = \sin x$ and we want to evaluate $(f + 1)(x)$, we can treat the constant 1 as a function that always returns 1. $(f + 1)(x) = f(x) + 1 = \sin x + 1$

Q9: What is the value of $(f \cdot g)(x)$ when $f(x) = \cos x$ and $g(x) = \sin x$?

A9: To evaluate $(f \cdot g)(x)$, we need to multiply the two functions together. $(f \cdot g)(x) = f(x) \cdot g(x) = \cos x \cdot \sin x = \sin x \cos x$

Q10: How do I evaluate a function operation with a logarithmic function?

A10: To evaluate a function operation with a logarithmic function, you can follow the same steps as evaluating a function operation with a polynomial function. For example, if we have the function $f(x) = \log x$ and we want to evaluate $(f + 1)(x)$, we can treat the constant 1 as a function that always returns 1. $(f + 1)(x) = f(x) + 1 = \log x + 1$

Conclusion

In this article, we answered some frequently asked questions related to function operations. We covered topics such as function addition and multiplication, evaluating function operations with multiple functions, and evaluating function operations with constants, rational functions, trigonometric functions, and logarithmic functions. We hope that this article has been helpful in understanding function operations and how to evaluate them.