To determine the values of [tex]\( f(4) \)[/tex] and [tex]\( g(-4) \)[/tex] using the given functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex], let's take it step by step.
First, we use the function [tex]\( f(x) = -5x - 1 \)[/tex] to find [tex]\( f(4) \)[/tex].
1. Substitute [tex]\( x = 4 \)[/tex] into the function [tex]\( f \)[/tex]:
[tex]\[
f(4) = -5(4) - 1
\][/tex]
2. Calculate the value inside the parentheses:
[tex]\[
-5(4) = -20
\][/tex]
3. Subtract 1 from -20:
[tex]\[
-20 - 1 = -21
\][/tex]
So,
[tex]\[
f(4) = -21
\][/tex]
Next, we use the function [tex]\( g(x) = -2x^3 - 5 \)[/tex] to find [tex]\( g(-4) \)[/tex].
1. Substitute [tex]\( x = -4 \)[/tex] into the function [tex]\( g \)[/tex]:
[tex]\[
g(-4) = -2(-4)^3 - 5
\][/tex]
2. First, calculate [tex]\( (-4)^3 \)[/tex]:
[tex]\[
(-4)^3 = -64
\][/tex]
3. Then multiply by -2:
[tex]\[
-2(-64) = 128
\][/tex]
4. Finally, subtract 5 from 128:
[tex]\[
128 - 5 = 123
\][/tex]
So,
[tex]\[
g(-4) = 123
\][/tex]
To summarize:
[tex]\[
f(4) = -21
\][/tex]
[tex]\[
g(-4) = 123
\][/tex]
