The problem provides a table of values for a function $f(x)$ and asks us to identify the table of values for its inverse function $f^{-1}(x)$.

1. Problem Description

The problem provides a table of values for a function $f(x)$ and asks us to identify the table of values for its inverse function $f^{-1}(x)$.

2. Solution Steps

To find the inverse function $f^{-1}(x)$, we need to swap the $x$ and $y$ values in the original table. That is, if the table for $f(x)$ contains the entry $(a,b)$, then the table for $f^{-1}(x)$ must contain the entry $(b,a)$.

The given table for $f(x)$ is:

$x$ | 3 | 4 | 9 | 11 | 16

---|---|---|---|---|---

$y$ | 1 | 6 | 7 | 13 | 14

Swapping $x$ and $y$ values, we obtain the table for $f^{-1}(x)$:

$x$ | 1 | 6 | 7 | 13 | 14

---|---|---|---|---|---

$y$ | 3 | 4 | 9 | 11 | 16

This is the last table in the answer choices.

3. Final Answer

The correct table for the inverse function $f^{-1}(x)$ is the one where $x$ and $y$ have been swapped. This is the option:

$x$ | 1 | 6 | 7 | 13 | 14

---|---|---|---|---|---

$y$ | 3 | 4 | 9 | 11 | 16