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
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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

Given functions: q(x) = x – 1 r(x) = 2x2 + 2

Answered: q (x) =x-1 2. r(x) =2x´+2 Find the…

Math

Algebra

q (x) =x-1 2. r(x) =2x´+2 Find the following.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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