Alright, let's work through this step by step.
We are given two functions:
[tex]\[ q(x) = 3x - 1 \][/tex]
[tex]\[ r(x) = -3x - 5 \][/tex]
We need to find the value of [tex]\( r(q(3)) \)[/tex].
### Step 1: Calculate [tex]\( q(3) \)[/tex]
First, let's evaluate the function [tex]\( q \)[/tex] at [tex]\( x = 3 \)[/tex].
[tex]\[ q(3) = 3(3) - 1 \][/tex]
Substituting 3 into the function [tex]\( q \)[/tex], we get:
[tex]\[ q(3) = 9 - 1 = 8 \][/tex]
So, [tex]\( q(3) = 8 \)[/tex].
### Step 2: Calculate [tex]\( r \left( q(3) \right) \)[/tex] or [tex]\( r(8) \)[/tex]
Next, we need to evaluate the function [tex]\( r \)[/tex] at [tex]\( x = 8 \)[/tex], since [tex]\( q(3) = 8 \)[/tex].
[tex]\[ r(8) = -3(8) - 5 \][/tex]
Substituting 8 into the function [tex]\( r \)[/tex], we get:
[tex]\[ r(8) = -24 - 5 = -29 \][/tex]
So, [tex]\( r(8) = -29 \)[/tex].
### Conclusion:
Therefore, the value of [tex]\( r(q(3)) \)[/tex] is:
[tex]\[ r(q(3)) = -29 \][/tex]
