Let's find [tex]\( f(5) \)[/tex] and [tex]\( g(-1) \)[/tex] using the given functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex].
### Calculating [tex]\( f(5) \)[/tex]:
Given the function [tex]\( f(x) = -6x - 7 \)[/tex]:
1. Substitute [tex]\( x = 5 \)[/tex] into the function:
[tex]\[
f(5) = -6(5) - 7
\][/tex]
2. Calculate the value:
[tex]\[
f(5) = -30 - 7
\][/tex]
3. Simplify the expression:
[tex]\[
f(5) = -37
\][/tex]
So, [tex]\( f(5) = -37 \)[/tex].
### Calculating [tex]\( g(-1) \)[/tex]:
Given the function [tex]\( g(x) = -3x^3 - x + 3 \)[/tex]:
1. Substitute [tex]\( x = -1 \)[/tex] into the function:
[tex]\[
g(-1) = -3(-1)^3 - (-1) + 3
\][/tex]
2. Calculate the value step-by-step:
[tex]\[
g(-1) = -3(-1) - (-1) + 3
\][/tex]
[tex]\[
g(-1) = 3 + 1 + 3
\][/tex]
3. Simplify the expression:
[tex]\[
g(-1) = 7
\][/tex]
So, [tex]\( g(-1) = 7 \)[/tex].
### Final Answers:
[tex]\[
f(5) = -37
\][/tex]
[tex]\[
g(-1) = 7
\][/tex]
