Let's fill in the values for the function [tex]\( f(x) = \frac{1}{x} \)[/tex] step-by-step.
Given the values:
[tex]\[
\begin{aligned}
&f(-1) = a = -1.0, \\
&f(-0.1) = b = -10.0, \\
&f(-0.01) = c = -100.0, \\
&f(-0.001) = d = -1000.0, \\
&f(0.001) = e = 1000.0, \\
&f(0.01) = f = 100.0, \\
&f(0.1) = g = 10.0, \\
&f(1) = h = 1.0.
\end{aligned}
\][/tex]
Here is the completed table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
-1 & $-1.0$ \\
\hline
-0.1 & $-10.0$ \\
\hline
-0.01 & $-100.0$ \\
\hline
-0.001 & $-1000.0$ \\
\hline
\end{tabular}
\][/tex]
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
0.001 & $ 1000.0$ \\
\hline
0.01 & $ 100.0$ \\
\hline
0.1 & $ 10.0$ \\
\hline
1 & $ 1.0$ \\
\hline
\end{tabular}
\][/tex]
So now we have:
[tex]\[
a = -1.0, \quad b = -10.0, \quad c = -100.0, \quad d = -1000.0, \quad e = 1000.0, \quad f = 100.0, \quad g = 10.0, \quad h = 1.0.
\][/tex]
