Question
Suppose that the functions \( q \) and \( r \) are defined as follows. \[ \begin{array}{l}q(x)=-2 x \\ r(x)=2 x^{2}-1 \\ \text { Find the following. } \\ (r \circ q)(-1)=\square\end{array} \]
Ask by Gonzalez Gray. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\((r \circ q)(-1) = 7\)
Solution
To find \((r \circ q)(-1)\), we perform the following steps:
1. **Compute \(q(-1)\):**
\[
q(x) = -2x \\
q(-1) = -2 \times (-1) = 2
\]
2. **Compute \(r(q(-1)) = r(2)\):**
\[
r(x) = 2x^2 - 1 \\
r(2) = 2 \times (2)^2 - 1 = 2 \times 4 - 1 = 8 - 1 = 7
\]
Therefore, \((r \circ q)(-1) = 7\).
**Answer:** \(7\)
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To find \((r \circ q)(-1)\), we start by calculating \(q(-1)\). Using the definition of \(q\), \[ q(-1) = -2(-1) = 2. \] Next, we need to find \(r(q(-1))\), which is \(r(2)\). Now, using the definition of \(r\), \[ r(2) = 2(2^2) - 1 = 2(4) - 1 = 8 - 1 = 7. \] Thus, \((r \circ q)(-1) = r(q(-1)) = r(2) = 7\). The final answer is \(\boxed{7}\).
