Suppose that the functions q and r are defined as follows **Composing Two Functions: Basic**### Presented ProblemSuppose that the functions \( q \) and \( r \) are defined as follows:\[ q(x) = x - 1 \]\[ r(x) = 2x^2 + 2 \]### TasksFind the following values:1. \[ (r \circ q)(-4) = \]2. \[ (q \circ r)(-4) = \]### Detailed ExplanationTo solve these compositions, we need to apply the concept of function composition. The composite function \( (r \circ q)(x) \) is evaluated as \( r(q(x)) \), and \( (q \circ r)(x) \) is evaluated as \( q(r(x)) \).1. **Evaluate \( (r \circ q)(-4) \)**: - First, find \( q(-4) \): \[ q(-4) = -4 - 1 = -5 \] - Next, use this result in \( r(x) \): \[ r(-5) = 2(-5)^2 + 2 = 2(25) + 2 = 50 + 2 = 52 \] - Therefore, \( (r \circ q)(-4) = 52 \). 2. **Evaluate \( (q \circ r)(-4) \)**: - First, find \( r(-4) \): \[ r(-4) = 2(-4)^2 + 2 = 2(16) + 2 = 32 + 2 = 34 \] - Next, use this result in \( q(x) \): \[ q(34) = 34 - 1 = 33 \] - Thus, \( (q \circ r)(-4) = 33 \).The values to be filled in the boxes are:1. \( (r \circ q)(-4) = 52 \)2. \( (q \circ r)(-4) = 33 \)### Visual UnderstandingThe image contains a simple interface with a space to input the calculated values and buttons likely for checking the answer, refreshing the question, and seeking help. The problem setup and the steps to solve these compositions have been provided in a textual format.

Name: Suppose that the functions q and r are defined as follows **Composing
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: Suppose that the functions q and r are defined as follows **Composing Two Functions: Basic**### Presented ProblemSuppose that the functions \( q \) and \( r \) are defined as follows:\[ q(x) = x - 1 \]\[ r(x) = 2x^2 + 2 \]### TasksFind the following