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].

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