consider the function represented in the table.\n| x | -10 | -20 | 0 | 5 | 8 |\n| f(x) | 3 | 8 | -2 | -4.5 |…

Explanation:

Step1: Determine points on the inverse function $f^{-1}$.

If $(x, y)$ is a point on the function $f$, then $(y, x)$ is a point on the inverse function $f^{-1}$. From the table, the points on $f$ are $(-10, 3), (-20, 8), (0, -2), (5, -4.5), (8, -6)$. Therefore, the points on $f^{-1}$ are $(3, -10), (8, -20), (-2, 0), (-4.5, 5), (-6, 8)$.

Step2: Find the minimum value of the inverse function $f^{-1}$.

The values of the inverse function are the second coordinates of the points on $f^{-1}$: $-10, -20, 0, 5, 8$. The minimum value among these is $-20$.

Step3: Identify the point on $f^{-1}$ corresponding to the minimum value.

The minimum value of $f^{-1}$ is $-20$. This occurs when the input to $f^{-1}$ is $8$. So, the point on the inverse function corresponding to its minimum value is $(8, -20)$.

Step4: Identify the corresponding point on the original function $f$.

The point $(8, -20)$ on $f^{-1}$ corresponds to the point $(-20, 8)$ on the original function $f$. This is the point on the given function $f$ that corresponds with the minimum value of its inverse function.

Answer:

A. $(-20, 8)$