Answer :
To fill in the table for the function [tex]\( g(x) = \sqrt[5]{x} \)[/tex], which finds the fifth root of [tex]\( x \)[/tex], we can simply evaluate [tex]\( g(x) \)[/tex] for each given value of [tex]\( x \)[/tex].
Here's the calculated value for each [tex]\( x \)[/tex]:
1. When [tex]\( x = -3125 \)[/tex], [tex]\( g(x) = -14.62 \)[/tex].
2. When [tex]\( x = -1024 \)[/tex], [tex]\( g(x) = -10.08 \)[/tex].
3. When [tex]\( x = -243 \)[/tex], [tex]\( g(x) = -6.24 \)[/tex].
4. When [tex]\( x = -32 \)[/tex], [tex]\( g(x) = -3.17 \)[/tex].
5. When [tex]\( x = -1 \)[/tex], [tex]\( g(x) = -1 \)[/tex].
6. When [tex]\( x = 0 \)[/tex], [tex]\( g(x) = 0 \)[/tex].
7. When [tex]\( x = 1 \)[/tex], [tex]\( g(x) = 1 \)[/tex].
8. When [tex]\( x = 32 \)[/tex], [tex]\( g(x) = 2 \)[/tex].
9. When [tex]\( x = 243 \)[/tex], [tex]\( g(x) = 3 \)[/tex].
10. When [tex]\( x = 1024 \)[/tex], [tex]\( g(x) = 4 \)[/tex].
11. When [tex]\( x = 3125 \)[/tex], [tex]\( g(x) = 5 \)[/tex].
Here's how you fill out the table on your sheet:
[tex]\[
\begin{array}{|c|c|}
\hline
x & g (x) \\
\hline
-3125 & -14.62 \\
\hline
-1024 & -10.08 \\
\hline
-243 & -6.24 \\
\hline
-32 & -3.17 \\
\hline
-1 & -1 \\
\hline
0 & 0 \\
\hline
1 & 1 \\
\hline
32 & 2 \\
\hline
243 & 3 \\
\hline
1024 & 4 \\
\hline
3125 & 5 \\
\hline
\end{array}
\][/tex]
This table represents the fifth root of each number [tex]\( x \)[/tex], which gives the values of the function [tex]\( g(x) = \sqrt[5]{x} \)[/tex].
Here's the calculated value for each [tex]\( x \)[/tex]:
1. When [tex]\( x = -3125 \)[/tex], [tex]\( g(x) = -14.62 \)[/tex].
2. When [tex]\( x = -1024 \)[/tex], [tex]\( g(x) = -10.08 \)[/tex].
3. When [tex]\( x = -243 \)[/tex], [tex]\( g(x) = -6.24 \)[/tex].
4. When [tex]\( x = -32 \)[/tex], [tex]\( g(x) = -3.17 \)[/tex].
5. When [tex]\( x = -1 \)[/tex], [tex]\( g(x) = -1 \)[/tex].
6. When [tex]\( x = 0 \)[/tex], [tex]\( g(x) = 0 \)[/tex].
7. When [tex]\( x = 1 \)[/tex], [tex]\( g(x) = 1 \)[/tex].
8. When [tex]\( x = 32 \)[/tex], [tex]\( g(x) = 2 \)[/tex].
9. When [tex]\( x = 243 \)[/tex], [tex]\( g(x) = 3 \)[/tex].
10. When [tex]\( x = 1024 \)[/tex], [tex]\( g(x) = 4 \)[/tex].
11. When [tex]\( x = 3125 \)[/tex], [tex]\( g(x) = 5 \)[/tex].
Here's how you fill out the table on your sheet:
[tex]\[
\begin{array}{|c|c|}
\hline
x & g (x) \\
\hline
-3125 & -14.62 \\
\hline
-1024 & -10.08 \\
\hline
-243 & -6.24 \\
\hline
-32 & -3.17 \\
\hline
-1 & -1 \\
\hline
0 & 0 \\
\hline
1 & 1 \\
\hline
32 & 2 \\
\hline
243 & 3 \\
\hline
1024 & 4 \\
\hline
3125 & 5 \\
\hline
\end{array}
\][/tex]
This table represents the fifth root of each number [tex]\( x \)[/tex], which gives the values of the function [tex]\( g(x) = \sqrt[5]{x} \)[/tex].
