Question
Suppose that the functions \( p \) and \( q \) are defined as follows. \[ \begin{array}{r}p(x)=-5 x+5 \\ q(x)=-2 x-2\end{array} \] Find the following. \( \begin{array}{r}(p \circ q)(-4)=\square\end{array} \)
Ask by Wood Bates. in the United States
Mar 19,2025
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Tutor-Verified Answer
Answer
\( (p \circ q)(-4) = -25 \)
Solution

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To find \((p \circ q)(-4)\), we first need to evaluate \(q(-4)\) and then plug that result into \(p\). Starting with \(q(-4)\): \[ q(x) = -2x - 2 \] \[ q(-4) = -2(-4) - 2 = 8 - 2 = 6 \] Now we have \(q(-4) = 6\). Next, we evaluate \(p(6)\): \[ p(x) = -5x + 5 \] \[ p(6) = -5(6) + 5 = -30 + 5 = -25 \] Thus, \((p \circ q)(-4) = p(q(-4)) = p(6) = -25\). The final answer is: \[ (p \circ q)(-4) = -25 \]