Question

Which ordered pair is on the inverse of f(x)?

(–4, –2)

(–2, –2)

(–1, –2)
A 2-column table with 5 rows titled Function. Column 1 is labeled x with entries negative 4, negative 2, 0, 2, 4. Column 2 is labeled f (x) with entries negative 2, negative 1, 0, 1, 2.

Answer 1

To find the ordered pair that is on the inverse of the function \( f(x) \), we must first understand what the inverse function does. The inverse function \( f^{-1}(x) \) essentially swaps the pairs of the original function \( f(x) \). Therefore, if an ordered pair \( (a, b) \) is on the function \( f(x) \), the pair \( (b, a) \) will be on its inverse.

From the table provided:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-4 & -2 \\
-2 & -1 \\
0 & 0 \\
2 & 1 \\
4 & 2 \\
\hline
\end{array}
\]

The pairs from this function \( f(x) \) are:

1. \( (-4, -2) \)
2. \( (-2, -1) \)
3. \( (0, 0) \)
4. \( (2, 1) \)
5. \( (4, 2) \)

Now, we can find the corresponding pairs for the inverse function:

1. \( f^{-1}(-2) = -4 \) → \( (-2, -4) \)
2. \( f^{-1}(-1) = -2 \) → \( (-1, -2) \)
3. \( f^{-1}(0) = 0 \) → \( (0, 0) \)
4. \( f^{-1}(1) = 2 \) → \( (1, 2) \)
5. \( f^{-1}(2) = 4 \) → \( (2, 4) \)

Now, we'll check the provided options against these pairs:

1. \( (-4, -2) \) → Not on the inverse
2. \( (-2, -2) \) → Not on the inverse
3. \( (-1, -2) \) → Matches with \( f^{-1}(-1) = -2 \)

Thus, the ordered pair that is on the inverse of \( f(x) \) is **(-1, -2)**.