Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.3 Inverse, Exponential, and Logarithmic Functions - 1.3 Exercises: 3

Answer

A function $f$ that is not one-to-one will fail the horizontal line test.

Work Step by Step

A function $f$ that is not one-to-one will have multiple $x$ values for one $y$ value, which means a horizontal line (a line parallel to the $x$-axis) connecting two points on the graph of said function can be drawn. Since this can be done, a function $f$ that is not one-to-one is said to fail the horizontal line test meaning it cannot have an inverse function.
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