Answered

Dive into the world of knowledge and get your queries resolved at IDNLearn.com. Get prompt and accurate answers to your questions from our community of knowledgeable experts.

The functions [tex]\( q \)[/tex] and [tex]\( r \)[/tex] are defined as:
[tex]\[
\begin{array}{l}
q(x) = 3x - 1 \\
r(x) = -3x - 5
\end{array}
\][/tex]

Find the value of [tex]\( r(q(3)) \)[/tex].
[tex]\[
r(q(3)) =
\][/tex]

Sagot :

GinnyAnsweridn
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]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.