Question
Suppose that the functions \( q \) and \( r \) are defined as follows. \[ \begin{array}{l}q(x)=-2 x \\ r(x)=2 x^{2}-1 \\ \text { Find the following. } \\ (r \circ q)(-1)=7 \\ (q \circ r)(-1)=\square\end{array} \]
Ask by Bond Goodwin. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\((q \circ r)(-1) = -2\)
Solution
To find \((q \circ r)(-1)\), we first need to evaluate \(r(-1)\) and then apply the function \(q\) to the result.
1. **Calculate \(r(-1)\):**
\[
r(x) = 2x^2 - 1
\]
\[
r(-1) = 2(-1)^2 - 1 = 2(1) - 1 = 2 - 1 = 1
\]
2. **Apply \(q\) to the result of \(r(-1)\):**
\[
q(x) = -2x
\]
\[
q(r(-1)) = q(1) = -2(1) = -2
\]
Therefore, \((q \circ r)(-1) = -2\).
**Answer:** \(-2\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find \((q \circ r)(-1)\), we need to first compute \(r(-1)\) and then apply the function \(q\) to the result. 1. Calculate \(r(-1)\): \[ r(-1) = 2(-1)^2 - 1 = 2(1) - 1 = 2 - 1 = 1 \] 2. Now, use the result from \(r(-1)\) to find \(q(r(-1)) = q(1)\): \[ q(1) = -2(1) = -2 \] Thus, \((q \circ r)(-1) = -2\).
