Answer :
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].
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].