Question
Suppose that the functions \( u \) and \( w \) are defined as follows \[ \begin{array}{l}u(x)=-2 x-2 \\ w(x)=-x^{2} \\ \text { Find the following. } \\ \qquad(w \circ u)(4)=\square\end{array} \]
Ask by Higgins Carroll. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\((w \circ u)(4) = -100\)
Solution
1. Compute \( u(4) \):
\[
u(4) = -2(4) - 2 = -8 - 2 = -10.
\]
2. Compute \( w(u(4)) \) by substituting the result into \( w(x) \):
\[
w(-10) = -(-10)^2 = -100.
\]
Thus, \((w \circ u)(4) = -100.\)
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Simplify this solution Bonus Knowledge
To find \((w \circ u)(4)\), we start by finding \(u(4)\) and then using that result to find \(w\) of the result. 1. Calculate \(u(4)\): \[ u(4) = -2(4) - 2 = -8 - 2 = -10 \] 2. Now, substitute \(-10\) into the function \(w\): \[ w(-10) = -(-10)^2 = -100 \] Therefore, \((w \circ u)(4) = -100\).
