Sure, let's solve the two parts of this question step-by-step.
1. Given [tex]\( f(x) = -3x - 2 \)[/tex], find the following:
### a. [tex]\( f(3) \)[/tex]
To find [tex]\( f(3) \)[/tex], we substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(3) = -3 \cdot 3 - 2 \][/tex]
First, we multiply [tex]\( -3 \)[/tex] by [tex]\( 3 \)[/tex]:
[tex]\[ -3 \cdot 3 = -9 \][/tex]
Next, we subtract [tex]\( 2 \)[/tex] from [tex]\( -9 \)[/tex]:
[tex]\[ -9 - 2 = -11 \][/tex]
So, [tex]\( f(3) = -11 \)[/tex].
### b. [tex]\( f(-1) \)[/tex]
To find [tex]\( f(-1) \)[/tex], we substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-1) = -3 \cdot (-1) - 2 \][/tex]
First, we multiply [tex]\( -3 \)[/tex] by [tex]\( -1 \)[/tex]:
[tex]\[ -3 \cdot (-1) = 3 \][/tex]
Next, we subtract [tex]\( 2 \)[/tex] from [tex]\( 3 \)[/tex]:
[tex]\[ 3 - 2 = 1 \][/tex]
So, [tex]\( f(-1) = 1 \)[/tex].
### Summary:
- [tex]\( f(3) = -11 \)[/tex]
- [tex]\( f(-1) = 1 \)[/tex]
We've found the values as required.
