The given image shows two tables: one for the function $f(x)$ and another for its inverse $f^{-1}(x)$.

From the tables:

• For $f(x)$, we have: \hline x & f(x) \\ \hline -2 & -5 \\ 0 & 1 \\ 1 & 4 \\ 2 & 7 \\ \hline \end{array}$$
• For $f^{-1}(x)$, we have: \hline x & f^{-1}(x) \\ \hline 7 & a \\ & \\ & \\ \hline \end{array}$$

We know that the inverse function $f^{-1}(x)$ reverses the inputs and outputs of the original function $f(x)$. This means that if $f(2) = 7$, then $f^{-1}(7) = 2$.

Thus, the value of $a$ is $2$.

Would you like further details or clarifications?

Here are five related questions for further exploration:

1. How do we determine the inverse of a function algebraically?
2. What are the conditions for a function to have an inverse?
3. Can all functions have