Sure! Let's evaluate the function [tex]\( f(x) = x^3 - 64 \)[/tex] at [tex]\( x = -4 \)[/tex].
1. Start by substituting [tex]\( x = -4 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(-4) = (-4)^3 - 64
\][/tex]
2. Compute [tex]\((-4)^3\)[/tex]:
[tex]\[
(-4)^3 = -4 \times -4 \times -4 = -64
\][/tex]
3. Substitute [tex]\(-64\)[/tex] into the equation:
[tex]\[
f(-4) = -64 - 64
\][/tex]
4. Finally, perform the subtraction:
[tex]\[
f(-4) = -128
\][/tex]
Therefore, the value of the function [tex]\( f(x) = x^3 - 64 \)[/tex] at [tex]\( x = -4 \)[/tex] is [tex]\( -128 \)[/tex].
