To evaluate [tex]\( g(-3) \)[/tex] for the function [tex]\( g(x) = x^3 + 2x^2 - x \)[/tex], we substitute [tex]\( x = -3 \)[/tex] into the function.
Step-by-step:
1. Substitute [tex]\( x = -3 \)[/tex] into the function:
[tex]\[
g(-3) = (-3)^3 + 2(-3)^2 - (-3)
\][/tex]
2. Calculate [tex]\( (-3)^3 \)[/tex]:
[tex]\[
(-3)^3 = -27
\][/tex]
3. Calculate [tex]\( 2(-3)^2 \)[/tex]:
[tex]\[
(-3)^2 = 9 \quad \text{(because the square of any number is positive)}
\][/tex]
[tex]\[
2 \cdot 9 = 18
\][/tex]
4. Calculate [tex]\( -(-3) \)[/tex]:
[tex]\[
-(-3) = 3
\][/tex]
5. Combine all the terms:
[tex]\[
g(-3) = -27 + 18 + 3
\][/tex]
6. Perform the addition and subtraction step-by-step:
[tex]\[
-27 + 18 = -9
\][/tex]
[tex]\[
-9 + 3 = -6
\][/tex]
So, the value of [tex]\( g(-3) \)[/tex] is [tex]\( \boxed{-6} \)[/tex].
