To solve the problem and find the value of [tex]\( f(0) \)[/tex], we need to refer to the values provided in the table. The table lists various values of [tex]\( x \)[/tex] and their corresponding function values [tex]\( f(x) \)[/tex].
Here is the table again for clarity:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
0 & 6 \\
\hline
2 & 7 \\
\hline
4 & 0 \\
\hline
7 & 5 \\
\hline
\end{tabular}
We need to determine [tex]\( f(0) \)[/tex]. To do this, look at the row where [tex]\( x = 0 \)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
0 & 6 \\
\hline
\end{array}
\][/tex]
From this row, we can see that [tex]\( f(0) = 6 \)[/tex].
Therefore, the correct answer is 6.
