To solve this problem, we need to evaluate the function [tex]\( f(x) = -x^3 + 7 \)[/tex] at [tex]\( x = -3 \)[/tex].
Step-by-Step Solution:
1. Identify the given function:
[tex]\[
f(x) = -x^3 + 7
\][/tex]
2. Substitute [tex]\( x = -3 \)[/tex] into the function:
[tex]\[
f(-3) = -(-3)^3 + 7
\][/tex]
3. Calculate [tex]\((-3)^3\)[/tex]:
[tex]\[
(-3)^3 = (-3) \times (-3) \times (-3) = -27
\][/tex]
4. Multiply the result by -1 (as indicated by the function):
[tex]\[
-(-27) = 27
\][/tex]
5. Add 7 to the result:
[tex]\[
27 + 7 = 34
\][/tex]
So, [tex]\( f(-3) = 34 \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{34}
\][/tex]
