**Problem Statement:**18) Find the inverse of the following function.\[ q(x) = \{(-4, -1), (0, -8), (-3, 4), (5, 2)\} \]**Solution:**To find the inverse of the function $ q(x) $, we need to swap the elements in each ordered pair. The inverse function, denoted as $ q^{-1}(x) $, will have the following pairs:\[ q^{-1}(x) = \{(-1, -4), (-8, 0), (4, -3), (2, 5)\} \]In summary, the inverse function is derived by exchanging the $ x $-coordinates with their corresponding $ y $-coordinates from the original function. This allows us to map each $ y $ back to its original $ x $ value.

Answered: 8) Find the inverse of the following…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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**Problem Statement:**

18) Find the inverse of the following function.

\[ q(x) = \{(-4, -1), (0, -8), (-3, 4), (5, 2)\} \]

**Solution:**

To find the inverse of the function $ q(x) $, we need to swap the elements in each ordered pair. The inverse function, denoted as $ q^{-1}(x) $, will have the following pairs:

\[ q^{-1}(x) = \{(-1, -4), (-8, 0), (4, -3), (2, 5)\} \]

In summary, the inverse function is derived by exchanging the $ x $-coordinates with their corresponding $ y $-coordinates from the original function. This allows us to map each $ y $ back to its original $ x $ value.

Expert Solution

Step 1

Given,

q(x) = {(-4 ,-1),(0,-8),(-3,4),(5,2)}

In the inverse function the range of the original function becomes the domain of the inverse function and the domain of the original function function becomes the range of the inverse function.

Domain and range of the q(x)

Domain corresponding range

-4 -1

0 -8

-3 4

5 2

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