Answer :
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]
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]
