https://file.aiquickdraw.com/mathbot/file/172688229952988lgcfuz.jpg

The problem asks to evaluate the function \(\left(\frac{f}{g}\right)(x)\) at \(x = 6\), given the functions:

- \( f(x) = -6x \)
- \( g(x) = |x + 7| \)
- \( h(x) = \frac{1}{x-2} \) (though \(h(x)\) seems irrelevant for this problem).

We are specifically asked to compute:

\[
\left(\frac{f}{g}\right)(6) = \frac{f(6)}{g(6)}.
\]

### Step 1: Compute \( f(6) \)
The function \( f(x) = -6x \), so:

\[
f(6) = -6(6) = -36.
\]

### Step 2: Compute \( g(6) \)
The function \( g(x) = |x + 7| \), so:

\[
g(6) = |6 + 7| = |13| = 13.
\]

### Step 3: Compute \(\frac{f(6)}{g(6)}\)
Now, divide \( f(6) \) by \( g(6) \):

\[
\frac{f(6)}{g(6)} = \frac{-36}{13}.
\]

Thus, the value of \(\left(\frac{f}{g}\right)(6)\) is \(-\frac{36}{13}\).

Would you like further explanation or details on this calculation?

Here are 5 related questions to consider:
1. How would the solution change if \( f(x) = -7x^2 \) instead of \( -6x \)?
2. What would happen if \( g(x) = |x - 2| \) instead of \( |x + 7| \)?
3. How do you simplify complex fractions like this one?
4. What are the implications of absolute values in functions like \( g(x) \)?
5. Can this process be applied to other types of functions, such as exponential or trigonometric?

**Tip:** Always remember that the absolute value of a number is never negative, which is crucial when evaluating functions like \( g(x) = |x + 7| \).

Evaluate the function (f/g)(x) for x = 6, given f(x) = -6x, g(x) = |x + 7|, and h(x) = 1/(x - 2).

Learn how to evaluate the function (f/g)(x) for x = 6 using the given functions f(x) = -6x and g(x) = |x + 7|. This problem covers key algebraic concepts such as functions and absolute value. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation