Question

x -7 -3 3 5 9
f(x) 5 1 9 3 -4
The table shows the function values of the one-to-one function f(x). Evaluate f(3)^−f^−1(5)−2f^−1(3)

(1 point)
f(3)−f^−1(5)−2f^−1(3)=

Answer 1

To evaluate the expression \( f(3) - f^{-1}(5) - 2f^{-1}(3) \), we first need to determine the values of \( f(3) \), \( f^{-1}(5) \), and \( f^{-1}(3) \) from the given table.

From the table:
- \( f(3) = 9 \) (since when \( x = 3, f(x) = 9 \))
- To find \( f^{-1}(5) \), we need to find the value of \( x \) for which \( f(x) = 5 \). Looking at the table, we see that \( f(-7) = 5 \), so \( f^{-1}(5) = -7 \).
- To find \( f^{-1}(3) \), we need to find the value of \( x \) for which \( f(x) = 3 \). Looking at the table, we see that \( f(5) = 3 \), so \( f^{-1}(3) = 5 \).

Now we can substitute these values into the expression:

\[
f(3) - f^{-1}(5) - 2f^{-1}(3) = 9 - (-7) - 2(5)
\]

Calculating it step by step:

1. Calculate \( 9 - (-7) \):
\[
9 + 7 = 16
\]

2. Calculate \( 2(5) \):
\[
2 \cdot 5 = 10
\]

3. Now substitute back:
\[
16 - 10 = 6
\]

Therefore, the final result is:

\[
f(3) - f^{-1}(5) - 2f^{-1}(3) = 6
\]