Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 10: 40


Example: f: {-1, 0, 1} $\rightarrow$ {0,1,2,3} defined by f(-1)=1, f(0)=0, f(1)=1. A function should only have one and only one image. But when D has 2 elements and R has 3 elements, two images should be there for a single preimage which is against the definition of a function. Therefore, such a function doesn't exist.

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