Question
\[ \qquad \begin{array}{l}u(x)=-x+1 \\ \qquad(x)=-2 x^{2}-1 \\ \text { Find the value of } u(w(-3))\end{array} \]
Ask by Alexander Simpson. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( u(w(-3)) = 20 \)
Solution
Let's solve the problem step by step.
Given the functions:
\[
u(x) = -x + 1
\]
\[
w(x) = -2x^{2} - 1
\]
We need to find the value of \( u(w(-3)) \).
1. **First, find \( w(-3) \):**
\[
w(-3) = -2(-3)^{2} - 1 = -2(9) - 1 = -18 - 1 = -19
\]
2. **Next, use this result to find \( u(w(-3)) = u(-19) \):**
\[
u(-19) = -(-19) + 1 = 19 + 1 = 20
\]
**Final Answer:** \( u(w(-3)) = 20 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the value of \( u(w(-3)) \), we first need to determine the value of \( w(-3) \) using the function \( w(x) = -2x^2 - 1 \). 1. Calculate \( w(-3) \): \[ w(-3) = -2(-3)^2 - 1 \] \[ = -2(9) - 1 \] \[ = -18 - 1 \] \[ = -19 \] 2. Now that we have \( w(-3) = -19 \), we need to calculate \( u(w(-3)) = u(-19) \) using the function \( u(x) = -x + 1 \). 3. Calculate \( u(-19) \): \[ u(-19) = -(-19) + 1 \] \[ = 19 + 1 \] \[ = 20 \] Thus, the value of \( u(w(-3)) \) is \( \boxed{20} \).
