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:

\[ \boxed{6} \]