If F ( X ) = 3 − 2 X F(x) = 3 - 2x F ( X ) = 3 − 2 X And G ( X ) = 1 X + 5 G(x) = \frac{1}{x+5} G ( X ) = X + 5 1 ​ , What Is The Value Of ( F G ) ( 8 \left(\frac{f}{g}\right)(8 ( G F ​ ) ( 8 ]?A. { -169$}$B. { -1$}$C. 13D. 104

If $f(x) = 3 - 2x$ and $g(x) = \frac{1}{x+5}$, what is the value of $\left(\frac{f}{g}\right)(8)$?

Understanding the Problem

To find the value of $\left(\frac{f}{g}\right)(8)$, we need to first understand what the notation $\left(\frac{f}{g}\right)(x)$ means. This notation represents the quotient of two functions, $f(x)$ and $g(x)$. In other words, it represents the function that results from dividing $f(x)$ by $g(x)$.

Finding the Quotient Function

To find the quotient function $\left(\frac{f}{g}\right)(x)$, we need to divide $f(x)$ by $g(x)$. This can be done by multiplying the numerator and denominator by the reciprocal of the denominator.

$$\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} = \frac{3 - 2x}{\frac{1}{x+5}}$$

To simplify this expression, we can multiply the numerator and denominator by $x+5$.

$$\left(\frac{f}{g}\right)(x) = \frac{(3 - 2x)(x+5)}{\frac{1}{x+5}(x+5)}$$

Simplifying the expression, we get:

$$\left(\frac{f}{g}\right)(x) = (3 - 2x)(x+5)$$

Evaluating the Quotient Function at $x=8$

Now that we have the quotient function, we can evaluate it at $x=8$.

$$\left(\frac{f}{g}\right)(8) = (3 - 2(8))(8+5)$$

Simplifying the expression, we get:

$$\left(\frac{f}{g}\right)(8) = (-13)(13)$$

Multiplying the numbers, we get:

$$\left(\frac{f}{g}\right)(8) = -169$$

Conclusion

Therefore, the value of $\left(\frac{f}{g}\right)(8)$ is $-169$.

Answer

The correct answer is:

• A. $-169$

Explanation

The quotient function $\left(\frac{f}{g}\right)(x)$ is found by dividing $f(x)$ by $g(x)$. To evaluate this function at $x=8$, we substitute $x=8$ into the quotient function and simplify the expression. The result is $-169$.

Step-by-Step Solution

1. Find the quotient function $\left(\frac{f}{g}\right)(x)$ by dividing $f(x)$ by $g(x)$.
2. Simplify the quotient function by multiplying the numerator and denominator by the reciprocal of the denominator.
3. Evaluate the quotient function at $x=8$ by substituting $x=8$ into the quotient function.
4. Simplify the expression to find the value of $\left(\frac{f}{g}\right)(8)$.

Final Answer

The final answer is $\boxed{-169}$.
If $f(x) = 3 - 2x$ and $g(x) = \frac{1}{x+5}$, what is the value of $\left(\frac{f}{g}\right)(8)$?

Understanding the Problem

To find the value of $\left(\frac{f}{g}\right)(8)$, we need to first understand what the notation $\left(\frac{f}{g}\right)(x)$ means. This notation represents the quotient of two functions, $f(x)$ and $g(x)$. In other words, it represents the function that results from dividing $f(x)$ by $g(x)$.

Finding the Quotient Function

To find the quotient function $\left(\frac{f}{g}\right)(x)$, we need to divide $f(x)$ by $g(x)$. This can be done by multiplying the numerator and denominator by the reciprocal of the denominator.

$$\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} = \frac{3 - 2x}{\frac{1}{x+5}}$$

To simplify this expression, we can multiply the numerator and denominator by $x+5$.

$$\left(\frac{f}{g}\right)(x) = \frac{(3 - 2x)(x+5)}{\frac{1}{x+5}(x+5)}$$

Simplifying the expression, we get:

$$\left(\frac{f}{g}\right)(x) = (3 - 2x)(x+5)$$

Evaluating the Quotient Function at $x=8$

Now that we have the quotient function, we can evaluate it at $x=8$.

$$\left(\frac{f}{g}\right)(8) = (3 - 2(8))(8+5)$$

Simplifying the expression, we get:

$$\left(\frac{f}{g}\right)(8) = (-13)(13)$$

Multiplying the numbers, we get:

$$\left(\frac{f}{g}\right)(8) = -169$$

Conclusion

Therefore, the value of $\left(\frac{f}{g}\right)(8)$ is $-169$.

Answer

The correct answer is:

• A. $-169$

Explanation

The quotient function $\left(\frac{f}{g}\right)(x)$ is found by dividing $f(x)$ by $g(x)$. To evaluate this function at $x=8$, we substitute $x=8$ into the quotient function and simplify the expression. The result is $-169$.

Step-by-Step Solution

1. Find the quotient function $\left(\frac{f}{g}\right)(x)$ by dividing $f(x)$ by $g(x)$.
2. Simplify the quotient function by multiplying the numerator and denominator by the reciprocal of the denominator.
3. Evaluate the quotient function at $x=8$ by substituting $x=8$ into the quotient function.
4. Simplify the expression to find the value of $\left(\frac{f}{g}\right)(8)$.

Final Answer

The final answer is $\boxed{-169}$.

Q&A

Q: What is the quotient function $\left(\frac{f}{g}\right)(x)$?

A: The quotient function $\left(\frac{f}{g}\right)(x)$ is found by dividing $f(x)$ by $g(x)$.

Q: How do you simplify the quotient function $\left(\frac{f}{g}\right)(x)$?

A: To simplify the quotient function, multiply the numerator and denominator by the reciprocal of the denominator.

Q: What is the value of $\left(\frac{f}{g}\right)(8)$?

A: The value of $\left(\frac{f}{g}\right)(8)$ is $-169$.

Q: How do you evaluate the quotient function at $x=8$?

A: To evaluate the quotient function at $x=8$, substitute $x=8$ into the quotient function and simplify the expression.

Q: What is the final answer to the problem?

A: The final answer is $\boxed{-169}$.

Additional Questions

Q: What is the difference between the quotient function and the product function?

A: The quotient function is found by dividing two functions, while the product function is found by multiplying two functions.

Q: How do you find the quotient function of two functions?

A: To find the quotient function, divide the first function by the second function.

Q: What is the importance of simplifying the quotient function?

A: Simplifying the quotient function makes it easier to evaluate and understand the function.

Conclusion

In this article, we have discussed the quotient function $\left(\frac{f}{g}\right)(x)$ and how to evaluate it at $x=8$. We have also answered some common questions related to the quotient function. The final answer to the problem is $\boxed{-169}$.