Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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 your visit. We are dedicated to helping you find the information you need, whenever you need it. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.