Answer :
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]
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]