Problem

Suppose that the functions $u$ and $w$ are defined as follows.
\[
\begin{array}{l}
u(x)=-x+2 \\
w(x)=3 x-4
\end{array}
\]
Find the following.
\[
\begin{array}{l}
(w \circ u)(-4)= \\
(u \circ w)(-4)=
\end{array}
\]

Answer

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Answer

So, the final answers are \((w \circ u)(-4) = \boxed{14}\) and \((u \circ w)(-4) = \boxed{18}\).

Steps

Step 1 :Let's first find the value of the function \(u(x)\) at \(x=-4\). So, \(u(-4) = -(-4) + 2 = 6\).

Step 2 :Next, we substitute this value into the function \(w(x)\) to find \((w \circ u)(-4)\). So, \((w \circ u)(-4) = w(u(-4)) = w(6) = 3*6 - 4 = 14\).

Step 3 :Now, let's find the value of the function \(w(x)\) at \(x=-4\). So, \(w(-4) = 3*(-4) - 4 = -16\).

Step 4 :Next, we substitute this value into the function \(u(x)\) to find \((u \circ w)(-4)\). So, \((u \circ w)(-4) = u(w(-4)) = u(-16) = -(-16) + 2 = 18\).

Step 5 :So, the final answers are \((w \circ u)(-4) = \boxed{14}\) and \((u \circ w)(-4) = \boxed{18}\).

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