To determine if the statement is true, we need to identify the [tex]\(x\)[/tex]-intercept of the function [tex]\(g(x)\)[/tex]. The [tex]\(x\)[/tex]-intercept is the value of [tex]\(x\)[/tex] at which [tex]\(g(x)\)[/tex] equals 0.
Given the table:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline
g(x) & -26 & -7 & 0 & 1 & 2 & 9 & 28 \\
\hline
\end{array}
\][/tex]
We look for the value of [tex]\(x\)[/tex] where [tex]\(g(x) = 0\)[/tex].
1. For [tex]\(x = -3\)[/tex], [tex]\(g(-3) = -26\)[/tex] (not zero).
2. For [tex]\(x = -2\)[/tex], [tex]\(g(-2) = -7\)[/tex] (not zero).
3. For [tex]\(x = -1\)[/tex], [tex]\(g(-1) = 0\)[/tex].
Here, [tex]\(g(x)\)[/tex] equals 0 when [tex]\(x = -1\)[/tex]. Therefore, the [tex]\(x\)[/tex]-intercept of [tex]\(g(x)\)[/tex] is [tex]\(x = -1\)[/tex].
The statement "The [tex]\(x\)[/tex]-intercept of [tex]\(f(x)\)[/tex] is equal to the [tex]\(x\)[/tex]-intercept of [tex]\(g(x)\)[/tex]" implies that there is an [tex]\(f(x)\)[/tex] with an [tex]\(x\)[/tex]-intercept equal to -1. Without information on [tex]\(f(x)\)[/tex], we cannot verify this part; however, the [tex]\(x\)[/tex]-intercept of [tex]\(g(x)\)[/tex] is accurately determined as [tex]\(x = -1\)[/tex].
Thus, the [tex]\(x\)[/tex]-intercept of [tex]\(g(x)\)[/tex] is [tex]\(-1\)[/tex].
