To solve the problem, we'll examine the given table, which provides values for the function [tex]\( f(x) \)[/tex] for specific values of [tex]\( x \)[/tex]. We are looking for the value of [tex]\( x \)[/tex] where [tex]\( f(x) = 2 \)[/tex].
Let's go through the table step-by-step:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & 0 \\
\hline
-1 & 1 \\
\hline
0 & 2 \\
\hline
1 & -2 \\
\hline
2 & -1 \\
\hline
\end{array}
\][/tex]
We need to find the [tex]\( x \)[/tex] value such that [tex]\( f(x) = 2 \)[/tex].
1. For [tex]\( x = -2 \)[/tex], [tex]\( f(-2) = 0 \)[/tex]. This is not equal to 2.
2. For [tex]\( x = -1 \)[/tex], [tex]\( f(-1) = 1 \)[/tex]. This is not equal to 2.
3. For [tex]\( x = 0 \)[/tex], [tex]\( f(0) = 2 \)[/tex]. This matches our desired value of 2.
4. For [tex]\( x = 1 \)[/tex], [tex]\( f(1) = -2 \)[/tex]. This is not equal to 2.
5. For [tex]\( x = 2 \)[/tex], [tex]\( f(2) = -1 \)[/tex]. This is not equal to 2.
We find that when [tex]\( x = 0 \)[/tex], the function [tex]\( f(x) \)[/tex] equals 2.
Thus, the correct answer is [tex]\( \boxed{0} \)[/tex].
