A table of values for a one-to-one function is given. Find the indicated value.

[tex]\[ f^{-1}(0)= \][/tex]

[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$x$ & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
$f(x)$ & 6 & 9 & 8 & 3 & 2 & 0 \\
\hline
\end{tabular}
\][/tex]



Answer :

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].