Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Exercise Set - Page 260: 123

Answer

$\left\{ \left( 4,\ -2 \right),\left( 1,\ -1 \right),\left( 1,\ 1 \right),\left( 4,\ 2 \right) \right\}$ The relation is not a function.

Work Step by Step

A function is defined to be a relation from a set A to a set B if each element in set A is assigned to a unique element in set B. Reverse each element of the ordered pair and get, $\left\{ \left( 4,\ -2 \right),\left( 1,\ -1 \right),\left( 1,\ 1 \right),\left( 4,\ 2 \right) \right\}$ Observe and see The element $1$ from the first component has two different values $-1,\ 1$. From the definition of the function, it implies that the mentioned relation is not a function. Hence, the reverse component of each ordered pair as mentioned in the question is not a function.
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