To find the value of the function [tex]\( f(x) = x^3 - 2x^2 + 5 \)[/tex] at [tex]\( x = -2 \)[/tex], we need to substitute [tex]\( -2 \)[/tex] into the function and simplify.
Let's start with the substitution:
[tex]\[ f(-2) = (-2)^3 - 2(-2)^2 + 5 \][/tex]
Now, evaluate each term step-by-step:
1. Calculate [tex]\( (-2)^3 \)[/tex]:
[tex]\[
(-2)^3 = -8
\][/tex]
2. Calculate [tex]\( (-2)^2 \)[/tex]:
[tex]\[
(-2)^2 = 4
\][/tex]
Then multiply this result by 2:
[tex]\[
2 \cdot 4 = 8
\][/tex]
3. Add 5 to the results from the previous steps:
[tex]\[
-8 - 8 + 5
\][/tex]
Combine these values:
[tex]\[
-8 - 8 = -16
\][/tex]
[tex]\[
-16 + 5 = -11
\][/tex]
Therefore, the value of [tex]\( f(-2) \)[/tex] is [tex]\( -11 \)[/tex].
So, the correct answer is:
4. [tex]\(-11\)[/tex]
