To solve for [tex]\( g(2) \)[/tex] given the function [tex]\( g(x) = 2x^3 - x + 8 \)[/tex], follow these steps:
1. Substitute [tex]\( x \)[/tex] with 2 in the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(2) = 2(2)^3 - 2 + 8
\][/tex]
2. Calculate the power term:
[tex]\[
(2)^3 = 8
\][/tex]
3. Multiply the result by 2:
[tex]\[
2 \cdot 8 = 16
\][/tex]
4. Substitute back into the equation:
[tex]\[
g(2) = 16 - 2 + 8
\][/tex]
5. Perform the addition and subtraction:
[tex]\[
16 - 2 = 14
\][/tex]
[tex]\[
14 + 8 = 22
\][/tex]
Thus, [tex]\( g(2) = 22 \)[/tex].
The answer tells us that when the input [tex]\( x \)[/tex] is 2, the output of the function [tex]\( g(x) \)[/tex] is 22. Therefore, [tex]\( g(2) \)[/tex] equals 22.
