Suppose that the functions \( q \) and \( r \) are defined as follows, \( \begin{array}{l}q(x)=-4 x+5 \\ r(x)=x+3 \\ \text { Find the following. } \\ (r \circ q)(2)=\square \\ (q \circ r)(2)=\square\end{array} \)

To solve for \( (r \circ q)(2) \) and \( (q \circ r)(2) \), we first need to understand what these compositions mean. 1. **Calculating \( (r \circ q)(2) \)**: This means we first apply \( q \) to \( 2 \), and then apply \( r \) to the result. \[ q(2) = -4(2) + 5 = -8 + 5 = -3 \] Now, apply \( r \) to \( -3 \): \[ r(-3) = -3 + 3 = 0 \] So, \( (r \circ q)(2) = 0 \). 2. **Calculating \( (q \circ r)(2) \)**: Here, we apply \( r \) to \( 2 \) first, and then apply \( q \) to that result. \[ r(2) = 2 + 3 = 5 \] Now, apply \( q \) to \( 5 \): \[ q(5) = -4(5) + 5 = -20 + 5 = -15 \] So, \( (q \circ r)(2) = -15 \). Putting it all together, we have: \[ (r \circ q)(2) = 0 \] \[ (q \circ r)(2) = -15 \]