To find the input value for which [tex]\( f(x) = g(x) \)[/tex], we can analyze the values of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] across the given inputs [tex]\( x \)[/tex].
Let's look at the tables provided:
For [tex]\( f(x) \)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & 3 \\
\hline
-1 & 3 \\
\hline
0 & 3 \\
\hline
1 & 3 \\
\hline
2 & 3 \\
\hline
3 & 3 \\
\hline
\end{array}
\][/tex]
For [tex]\( g(x) \)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & g(x) \\
\hline
-2 & 4 \\
\hline
-1 & 3 \\
\hline
0 & 2 \\
\hline
1 & 1 \\
\hline
2 & 0 \\
\hline
3 & -1 \\
\hline
\end{array}
\][/tex]
We need to find the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = g(x) \)[/tex].
- At [tex]\( x = -2 \)[/tex], [tex]\( f(-2) = 3 \)[/tex] and [tex]\( g(-2) = 4 \)[/tex] (not equal)
- At [tex]\( x = -1 \)[/tex], [tex]\( f(-1) = 3 \)[/tex] and [tex]\( g(-1) = 3 \)[/tex] (equal)
- At [tex]\( x = 0 \)[/tex], [tex]\( f(0) = 3 \)[/tex] and [tex]\( g(0) = 2 \)[/tex] (not equal)
- At [tex]\( x = 1 \)[/tex], [tex]\( f(1) = 3 \)[/tex] and [tex]\( g(1) = 1 \)[/tex] (not equal)
- At [tex]\( x = 2 \)[/tex], [tex]\( f(2) = 3 \)[/tex] and [tex]\( g(2) = 0 \)[/tex] (not equal)
- At [tex]\( x = 3 \)[/tex], [tex]\( f(3) = 3 \)[/tex] and [tex]\( g(3) = -1 \)[/tex] (not equal)
The value of [tex]\( x \)[/tex] for which [tex]\( f(x) = g(x) \)[/tex] is:
[tex]\[
x = -1
\][/tex]
