Question
Suppose that the functions \( q \) and \( r \) are defined as follows. \[ \begin{array}{l}q(x)=3 x-2 \\ r(x)=4 x+5\end{array} \] Find the following. \[ (r \circ q)(-1)=\square \]
Ask by Curry Hills. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\((r \circ q)(-1) = -15\)
Solution
To find \((r \circ q)(-1)\), we need to evaluate the functions \(q\) and \(r\) in succession.
1. **First, evaluate \(q(-1)\):**
\[
q(x) = 3x - 2 \\
q(-1) = 3(-1) - 2 = -3 - 2 = -5
\]
2. **Next, use the result from \(q(-1)\) as the input for \(r\):**
\[
r(x) = 4x + 5 \\
r(-5) = 4(-5) + 5 = -20 + 5 = -15
\]
Therefore, \((r \circ q)(-1) = -15\).
\[
\rboxed{-15}
\]
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Simplify this solution Bonus Knowledge
To find \((r \circ q)(-1)\), we need to first evaluate \(q(-1)\) and then substitute that result into \(r\). Starting with \(q(-1)\): \[ q(-1) = 3(-1) - 2 = -3 - 2 = -5 \] Now we can find \(r(q(-1)) = r(-5)\): \[ r(-5) = 4(-5) + 5 = -20 + 5 = -15 \] Therefore, \((r \circ q)(-1) = -15\). The final answer is: \[ (r \circ q)(-1) = -15 \]
