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

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

Algebra and Trigonometry (6th Edition)
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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Suppose that the functions q and r are defined as follows

**Composing Two Functions: Basic** ### Presented Problem Suppose that the functions \( q \) and \( r \) are defined as follows: \[ q(x) = x - 1 \] \[ r(x) = 2x^2 + 2 \] ### Tasks Find the following values: 1. \[ (r \circ q)(-4) = \] 2. \[ (q \circ r)(-4) = \] ### Detailed Explanation To 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 Understanding The 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.
Transcribed Image Text:**Composing Two Functions: Basic** ### Presented Problem Suppose that the functions \( q \) and \( r \) are defined as follows: \[ q(x) = x - 1 \] \[ r(x) = 2x^2 + 2 \] ### Tasks Find the following values: 1. \[ (r \circ q)(-4) = \] 2. \[ (q \circ r)(-4) = \] ### Detailed Explanation To 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 Understanding The 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.
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