To solve for \( f(-2) \) when \( f(x) = x^3 - 2x - 1 \):
1. Start with the given function:
[tex]\[
f(x) = x^3 - 2x - 1
\][/tex]
2. Substitute \( x = -2 \) into the function:
[tex]\[
f(-2) = (-2)^3 - 2(-2) - 1
\][/tex]
3. Calculate each term individually:
- First term: \((-2)^3\)
[tex]\[
(-2)^3 = -8
\][/tex]
- Second term: \(-2(-2)\)
[tex]\[
-2(-2) = 4
\][/tex]
- Third term: \(-1\) remains \(-1\)
4. Combine these results:
[tex]\[
f(-2) = -8 + 4 - 1
\][/tex]
5. Perform the addition and subtraction:
[tex]\[
-8 + 4 = -4
\][/tex]
[tex]\[
-4 - 1 = -5
\][/tex]
Therefore, [tex]\( f(-2) = -5 \)[/tex].
