Question
\[ \begin{array}{l}q(x)=2 x+1 \\ r(x)=-x^{2}+1\end{array} \] Find the value of \( q(r(-2)) \)
Ask by Pollard Wood. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( q(r(-2)) = -5 \)
Solution
To find the value of \( q(r(-2)) \), follow these steps:
1. **Compute \( r(-2) \):**
\[
r(x) = -x^2 + 1
\]
Substitute \( x = -2 \):
\[
r(-2) = -(-2)^2 + 1 = -4 + 1 = -3
\]
2. **Compute \( q(r(-2)) = q(-3) \):**
\[
q(x) = 2x + 1
\]
Substitute \( x = -3 \):
\[
q(-3) = 2(-3) + 1 = -6 + 1 = -5
\]
**Final Answer:** \(-5\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find the value of \( q(r(-2)) \), we first need to evaluate \( r(-2) \). Using the function \( r(x) = -x^2 + 1 \): \[ r(-2) = -(-2)^2 + 1 = -4 + 1 = -3 \] Now that we have \( r(-2) = -3 \), we can substitute this value into the function \( q(x) \). Using the function \( q(x) = 2x + 1 \): \[ q(-3) = 2(-3) + 1 = -6 + 1 = -5 \] Therefore, the value of \( q(r(-2)) \) is \[ \boxed{-5} \]
