https://file.aiquickdraw.com/mathbot/file/17254843018851ux3fo0i.jpg

Let's analyze the table and solve the questions based on it. The table provides values for \( x \) and the corresponding function values \( f(x) \).

Here's the table extracted from the image:

\[
\begin{array}{c|c}
x & f(x) \\
\hline
0 & 8 \\
1 & 6 \\
2 & 4 \\
3 & 2 \\
4 & 0 \\
5 & -2 \\
6 & -4 \\
7 & -6 \\
8 & -8 \\
9 & -10 \\
\end{array}
\]

Now, let's answer the questions:

1. **\( f(2) = \)**  
   To find \( f(2) \), look for the value of \( f(x) \) when \( x = 2 \).  
   \[
   f(2) = 4
   \]

2. **If \( f(x) = 0 \), then \( x = \)**  
   To find \( x \) when \( f(x) = 0 \), look for the value of \( x \) corresponding to \( f(x) = 0 \).  
   \[
   f(x) = 0 \text{ when } x = 4
   \]

3. **\( f^{-1}(-8) = \)**  
   The inverse function \( f^{-1}(y) \) gives the value of \( x \) such that \( f(x) = y \).  
   \[
   f^{-1}(-8) = 8
   \]

4. **If \( f^{-1}(x) = 7 \), then \( x = \)**  
   If \( f^{-1}(x) = 7 \), then \( f(7) = x \). Look for the value of \( f(7) \).  
   \[
   f(7) = -6 \text{, so } x = -6
   \]

Here are the answers:

1. \( f(2) = 4 \)
2. If \( f(x) = 0 \), then \( x = 4 \)
3. \( f^{-1}(-8) = 8 \)
4. If \( f^{-1}(x) = 7 \), then \( x = -6 \)

Would you like further details on any of these solutions or explanations?

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**Related Questions:**
1. What is \( f^{-1}(0) \)?
2. Find \( f(9) \).
3. If \( f^{-1}(x) = 4 \), what is \( x \)?
4. Calculate \( f^{-1}(-2) \).
5. Determine \( f(0) \).

**Tip:** When working with inverse functions, remember that \( f^{-1}(y) = x \) means \( f(x) = y \). This helps you find the input \( x \) that corresponds to a given output \( y \).

Use the table below to fill in the missing values:

1. f(2) = ?
2. If f(x) = 0, then x = ?
3. f^(-1)(-8) = ?
4. If f^(-1)(x) = 7, then x = ?

Learn how to solve function and inverse function problems using a table of values. This example covers finding specific function values, determining corresponding inputs for given outputs, and solving inverse functions. Ideal for Grades 9-10.

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