### Problem Statement**7) Use the table and the fact that \( f(x) \) is invertible and differentiable everywhere to find:**\[ \begin{array}{|c|c|c|}\hlinex & f(x) & f'(x) \\\hline3 & 1 & 7 \\\hline6 & 2 & 10 \\\hline9 & 3 & 5 \\\hline\end{array}\]**a) \( f^{-1}(3) = \)****b) \( f'(9) = \)****c) \( (f^{-1})'(3) = \)**### Explanation of TableThe table provided consists of three columns:- The first column represents the values of \( x \).- The second column represents the corresponding values of \( f(x) \) for each \( x \).- The third column represents the derivative of the function \( f(x) \), denoted as \( f'(x) \).### RequirementsTo solve the given problem, you will need to:**a) Determine the value of the inverse function \( f^{-1}(x) \) at \( x = 3 \).**Since \( f(x) = 3 \) when \( x = 9 \) (from the table), this means \( f^{-1}(3) = 9 \).**b) Determine the value of the derivative function \( f'(x) \) at \( x = 9 \).**From the table, \( f'(9) = 5 \).**c) Determine the value of the derivative of the inverse function \( (f^{-1})'(x) \) at \( x = 3 \).**Using the formula for the derivative of an inverse function:\[ (f^{-1})'(y) = \frac{1}{f'(f^{-1}(y))} \]First, we need to find \( f^{-1}(3) \), which we've already determined as \( 9 \). Now, use the value of \( f'(9) \):\[ (f^{-1})'(3) = \frac{1}{f'(9)} = \frac{1}{5} \]### Solutions**a) \( f^{-1}(3) = 9 \)**

Name: ### Problem Statement**7) Use the table and the fact that \( f(x) \)
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: ### Problem Statement**7) Use the table and the fact that \( f(x) \) is invertible and differentiable everywhere to find:**\[ \begin{array}{|c|c|c|}\hlinex & f(x) & f'(x) \\\hline3 & 1 & 7 \\\hline6 & 2 & 10 \\\hline9 & 3 & 5 \\\hline\end{array}\]**