Question
\[ \begin{array}{l}q(x)=-x-1 \\ r(x)=2 x^{2}+2\end{array} \] Find the value of \( r(q(4)) \)
Ask by Nichols Santiago. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( r(q(4)) = 52 \)
Solution
To find \( r(q(4)) \), follow these steps:
1. **Calculate \( q(4) \):**
\[
q(x) = -x - 1
\]
Plug in \( x = 4 \):
\[
q(4) = -4 - 1 = -5
\]
2. **Calculate \( r(q(4)) = r(-5) \):**
\[
r(x) = 2x^2 + 2
\]
Plug in \( x = -5 \):
\[
r(-5) = 2(-5)^2 + 2 = 2(25) + 2 = 50 + 2 = 52
\]
**Final Answer:** \( 52 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Let's first calculate \( q(4) \) using the function \( q(x) = -x - 1 \). Substituting \( x = 4 \): \[ q(4) = -4 - 1 = -5 \] Next, we will substitute \( q(4) \) into \( r(x) \) to find \( r(q(4)) = r(-5) \) using the function \( r(x) = 2x^2 + 2 \). Substituting \( x = -5 \): \[ r(-5) = 2(-5)^2 + 2 = 2(25) + 2 = 50 + 2 = 52 \] Thus, the value of \( r(q(4)) \) is \( \boxed{52} \).
