Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Let's analyze the given functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] at different points [tex]\( x \)[/tex]. We need to determine the corresponding values for [tex]\( h(x) = f(x) + g(x) \)[/tex].
The given table is:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline $x$ & $f(x)$ & $g(x)$ & $h(x) = f(x) + g(x)$ \\ \hline 1 & $3 \frac{1}{2}$ & 1 & \\ \hline 2 & 4 & $\frac{1}{4}$ & \\ \hline 3 & $4 \frac{1}{2}$ & $\frac{1}{9}$ & \\ \hline 4 & 5 & $\frac{1}{16}$ & \\ \hline \end{tabular} \][/tex]
We need to calculate the values of [tex]\( h(x) \)[/tex] for each [tex]\( x \)[/tex].
For [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = 3 \frac{1}{2} = 3 + \frac{1}{2} = 3.5 \][/tex]
[tex]\[ g(1) = 1 \][/tex]
[tex]\[ h(1) = f(1) + g(1) = 3.5 + 1 = 4.5 \][/tex]
For [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 4 \][/tex]
[tex]\[ g(2) = \frac{1}{4} = 0.25 \][/tex]
[tex]\[ h(2) = f(2) + g(2) = 4 + 0.25 = 4.25 \][/tex]
For [tex]\( x = 3 \)[/tex]:
[tex]\[ f(3) = 4 \frac{1}{2} = 4 + \frac{1}{2} = 4.5 \][/tex]
[tex]\[ g(3) = \frac{1}{9} \approx 0.1111111111111111 \][/tex]
[tex]\[ h(3) = f(3) + g(3) \approx 4.5 + 0.1111111111111111 \approx 4.611111111111111 \][/tex]
For [tex]\( x = 4 \)[/tex]:
[tex]\[ f(4) = 5 \][/tex]
[tex]\[ g(4) = \frac{1}{16} = 0.0625 \][/tex]
[tex]\[ h(4) = f(4) + g(4) = 5 + 0.0625 = 5.0625 \][/tex]
So, the completed table should be:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline $x$ & $f(x)$ & $g(x)$ & $h(x) = f(x) + g(x)$ \\ \hline 1 & $3 \frac{1}{2}$ & 1 & 4.5 \\ \hline 2 & 4 & $\frac{1}{4}$ & 4.25 \\ \hline 3 & $4 \frac{1}{2}$ & $\frac{1}{9}$ & 4.611111111111111 \\ \hline 4 & 5 & $\frac{1}{16}$ & 5.0625 \\ \hline \end{tabular} \][/tex]
Therefore, the values that complete the table for [tex]\( h(x) \)[/tex] are:
[tex]\[ \begin{tabular}{|c|} \hline $h(x) = f(x) + g(x)$ \\ \hline 4.5 \\ \hline 4.25 \\ \hline 4.611111111111111 \\ \hline 5.0625 \\ \hline \end{tabular} \][/tex]
The given table is:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline $x$ & $f(x)$ & $g(x)$ & $h(x) = f(x) + g(x)$ \\ \hline 1 & $3 \frac{1}{2}$ & 1 & \\ \hline 2 & 4 & $\frac{1}{4}$ & \\ \hline 3 & $4 \frac{1}{2}$ & $\frac{1}{9}$ & \\ \hline 4 & 5 & $\frac{1}{16}$ & \\ \hline \end{tabular} \][/tex]
We need to calculate the values of [tex]\( h(x) \)[/tex] for each [tex]\( x \)[/tex].
For [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = 3 \frac{1}{2} = 3 + \frac{1}{2} = 3.5 \][/tex]
[tex]\[ g(1) = 1 \][/tex]
[tex]\[ h(1) = f(1) + g(1) = 3.5 + 1 = 4.5 \][/tex]
For [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 4 \][/tex]
[tex]\[ g(2) = \frac{1}{4} = 0.25 \][/tex]
[tex]\[ h(2) = f(2) + g(2) = 4 + 0.25 = 4.25 \][/tex]
For [tex]\( x = 3 \)[/tex]:
[tex]\[ f(3) = 4 \frac{1}{2} = 4 + \frac{1}{2} = 4.5 \][/tex]
[tex]\[ g(3) = \frac{1}{9} \approx 0.1111111111111111 \][/tex]
[tex]\[ h(3) = f(3) + g(3) \approx 4.5 + 0.1111111111111111 \approx 4.611111111111111 \][/tex]
For [tex]\( x = 4 \)[/tex]:
[tex]\[ f(4) = 5 \][/tex]
[tex]\[ g(4) = \frac{1}{16} = 0.0625 \][/tex]
[tex]\[ h(4) = f(4) + g(4) = 5 + 0.0625 = 5.0625 \][/tex]
So, the completed table should be:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline $x$ & $f(x)$ & $g(x)$ & $h(x) = f(x) + g(x)$ \\ \hline 1 & $3 \frac{1}{2}$ & 1 & 4.5 \\ \hline 2 & 4 & $\frac{1}{4}$ & 4.25 \\ \hline 3 & $4 \frac{1}{2}$ & $\frac{1}{9}$ & 4.611111111111111 \\ \hline 4 & 5 & $\frac{1}{16}$ & 5.0625 \\ \hline \end{tabular} \][/tex]
Therefore, the values that complete the table for [tex]\( h(x) \)[/tex] are:
[tex]\[ \begin{tabular}{|c|} \hline $h(x) = f(x) + g(x)$ \\ \hline 4.5 \\ \hline 4.25 \\ \hline 4.611111111111111 \\ \hline 5.0625 \\ \hline \end{tabular} \][/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.