To find [tex]\( f(3) \)[/tex] and [tex]\( g(-4) \)[/tex] using the given functions [tex]\( f(x) = -4x + 4 \)[/tex] and [tex]\( g(x) = -2x^3 - 3 \)[/tex], follow the steps below for each function.
### Step-by-Step Solution
1. Calculate [tex]\( f(3) \)[/tex]:
The function [tex]\( f(x) = -4x + 4 \)[/tex].
Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = -4(3) + 4
\][/tex]
Simplify the expression inside the parentheses first:
[tex]\[
f(3) = -12 + 4
\][/tex]
Finally, combine the terms:
[tex]\[
f(3) = -8
\][/tex]
So, [tex]\( f(3) = -8 \)[/tex].
2. Calculate [tex]\( g(-4) \)[/tex]:
The function [tex]\( g(x) = -2x^3 - 3 \)[/tex].
Substitute [tex]\( x = -4 \)[/tex] into the function:
[tex]\[
g(-4) = -2(-4)^3 - 3
\][/tex]
Calculate the cube of [tex]\(-4\)[/tex]:
[tex]\[
(-4)^3 = -64
\][/tex]
Substitute [tex]\( -64 \)[/tex] back into the function:
[tex]\[
g(-4) = -2(-64) - 3
\][/tex]
Multiply the constants:
[tex]\[
-2 \cdot -64 = 128
\][/tex]
Finally, combine the terms:
[tex]\[
g(-4) = 128 - 3
\][/tex]
[tex]\[
g(-4) = 125
\][/tex]
So, [tex]\( g(-4) = 125 \)[/tex].
### Final Answers
[tex]\[
f(3) = -8
\][/tex]
[tex]\[
g(-4) = 125
\][/tex]
