Based on the graph provided, let us analyze the functions and fill in the missing values.

Step-by-step Explanation:

1. $f(0)$: To find $f(0)$, locate where $x = 0$ on the graph and check the corresponding $y$-value. From the graph, when $x = 0$, $f(x) = 4$.

   $f(0) = 4$

2. $f(x) = 0, x =$: To find when $f(x) = 0$, look at the x-coordinate where the graph crosses the x-axis. From the graph, this occurs when $x = 4$.

   $f(x) = 0, x = 4$

3. $f^{-1}(0)$: The inverse $f^{-1}(x)$ swaps the roles of $x$ and $y$. To find $f^{-1}(0)$, check where $f(x) = 0$ (this is equivalent to when $x = 4$ in the original function).

   $f^{-1}(0) = 4$

4. $f^{-1}(x) = 0, x =$: To find when the inverse of $f(x)$ equals 0, check where $x = 0$ in the original function. From the graph, this corresponds to $f(0) = 4$. Swapping $x$ and $y$, the inverse function is 0 when $x = 4$.

   $f^{-1}(x) = 0, x = 0$

Final Answers:

1. $f(0) = 4$
2. $f(x) = 0, x = 4$
3. $f^{-1}(0) = 4$
4. $f^{-1}(x) = 0, x = 0$

Let me know if you'd like further explanation or clarification! Here are some related questions for exploration:

1. What is the slope of the function $f(x)$ based on the graph?
2. How can you verify your answers for $f^{-1}(x)$ using algebra?
3. What does the inverse function geometrically represent on the graph?
4. Can you write an equation for $f(x)$ using the points provided?
5. How would the graph of $f^{-1}(x)$ look in comparison to $f(x)$?

Tip: When working with inverses, remember they are reflections across the line $y = x$. This can help visualize relationships between $f(x)$ and $f^{-1}(x)$.