Sure, let's solve for [tex]\( f(-3) \)[/tex] and [tex]\( g(-2) \)[/tex] using the given functions step-by-step.
Starting with [tex]\( f(x) = 5x + 4 \)[/tex]:
1. To find [tex]\( f(-3) \)[/tex], substitute [tex]\( x = -3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(-3) = 5(-3) + 4
\][/tex]
2. Now, calculate the value:
[tex]\[
f(-3) = -15 + 4
\][/tex]
3. Simplify the expression:
[tex]\[
f(-3) = -11
\][/tex]
Next, for [tex]\( g(x) = 3x^3 + 5 \)[/tex]:
1. To find [tex]\( g(-2) \)[/tex], substitute [tex]\( x = -2 \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(-2) = 3(-2)^3 + 5
\][/tex]
2. Now, calculate the value of [tex]\((-2)^3\)[/tex]:
[tex]\[
(-2)^3 = -8
\][/tex]
3. Substitute back into the function:
[tex]\[
g(-2) = 3(-8) + 5
\][/tex]
4. Calculate the resulting value:
[tex]\[
g(-2) = -24 + 5
\][/tex]
5. Simplify the expression:
[tex]\[
g(-2) = -19
\][/tex]
So, the solutions are:
[tex]\[
f(-3) = -11
\][/tex]
[tex]\[
g(-2) = -19
\][/tex]
