https://file.aiquickdraw.com/mathbot/file/1726679463646bpy29lsa.jpg

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:
  \[
  \begin{array}{|c|c|}
  \hline
  x & f(x) \\
  \hline
  -2 & -5 \\
  0 & 1 \\
  1 & 4 \\
  2 & 7 \\
  \hline
  \end{array}
  \]
  
- For \( f^{-1}(x) \), we have:
  \[
  \begin{array}{|c|c|}
  \hline
  x & f^{-1}(x) \\
  \hline
  7 & a \\
  &  \\
  &  \\
  \hline
  \end{array}
  \]

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

The tables represent a function and its inverse. What is the value of a?

Learn how to find the inverse of a function using a table. This problem involves determining the relationship between function and inverse function mappings and is suitable for students in Grades 9-12.

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