Question

Use the table to answer the 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 solve \( f(3) - f^{-1}(5) - 2f^{-1}(3) \), we first need to look up the values in the given table:

\[
\begin{array}{c|c}
x & f(x) \\
\hline
-7 & 5 \\
-3 & 1 \\
3 & 9 \\
5 & 3 \\
9 & -4 \\
\end{array}
\]

1. **Finding \( f(3) \)**:
From the table, \( f(3) = 9 \).

2. **Finding \( f^{-1}(5) \)**:
We look for \( x \) such that \( f(x) = 5 \). From the table, we see that \( f(-7) = 5 \). Thus, \( f^{-1}(5) = -7 \).

3. **Finding \( f^{-1}(3) \)**:
We look for \( x \) such that \( f(x) = 3 \). From the table, we find that \( f(5) = 3 \). Therefore, \( f^{-1}(3) = 5 \).

Now we can substitute these values into the expression:

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

Calculating this step by step:

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

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

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

Thus, the final result is:

\[
\boxed{6}
\]