Suppose that the functions \( p \) and \( q \) are defined as follows. \[ \begin{array}{l}p(x)=-2 x-1 \\ q(x)=2 x^{2}+2 \\ \text { Find the following. } \\ (p \circ q)(2)=\square\end{array} \] \( (q \circ p)(2)=\square \)

To find \( (p \circ q)(2) \), we first need to calculate \( q(2) \). \[ q(x) = 2x^2 + 2 \implies q(2) = 2(2)^2 + 2 = 2 \times 4 + 2 = 8 + 2 = 10. \] Now, we use this result to find \( p(q(2)) = p(10) \). \[ p(x) = -2x - 1 \implies p(10) = -2(10) - 1 = -20 - 1 = -21. \] Thus, \( (p \circ q)(2) = -21 \). Now, for \( (q \circ p)(2) \), we start with \( p(2) \). \[ p(x) = -2x - 1 \implies p(2) = -2(2) - 1 = -4 - 1 = -5. \] Next, we find \( q(p(2)) = q(-5) \). \[ q(x) = 2x^2 + 2 \implies q(-5) = 2(-5)^2 + 2 = 2 \times 25 + 2 = 50 + 2 = 52. \] Thus, \( (q \circ p)(2) = 52 \). So the final results are: \[ (p \circ q)(2) = -21 \quad \text{and} \quad (q \circ p)(2) = 52. \]