To find the indicated value [tex]\( f^{-1}(0) \)[/tex], we need to determine which [tex]\( x \)[/tex]-value corresponds to [tex]\( f(x) = 0 \)[/tex] from the given table.
Here is a step-by-step solution:
1. Understand the Problem: We need to find the value of [tex]\( x \)[/tex] for which the function [tex]\( f(x) \)[/tex] is equal to 0. This value is given by [tex]\( f^{-1}(0) \)[/tex].
2. Look at the Table: The table provided lists values of [tex]\( x \)[/tex] and their corresponding function values [tex]\( f(x) \)[/tex].
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
f(x) & 6 & 9 & 8 & 3 & 2 & 0 \\
\hline
\end{array}
\][/tex]
3. Identify [tex]\( f(x) = 0 \)[/tex]: We are looking for the row in which the value of [tex]\( f(x) \)[/tex] is 0.
4. Read Corresponding [tex]\( x \)[/tex]-value: From the table, when [tex]\( f(x) = 0 \)[/tex], it corresponds to [tex]\( x = 6 \)[/tex].
Hence, [tex]\( x = 6 \)[/tex] is the value that makes [tex]\( f(x) = 0 \)[/tex]. Thus,
[tex]\[ f^{-1}(0) = 6 \][/tex]
So the indicated value [tex]\( f^{-1}(0) \)[/tex] is [tex]\( 6 \)[/tex].
