Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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 :

GinnyAnswer
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 trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.