Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.8 - One-to-One Functions and Their Inverses - 2.8 Exercises - Page 225: 4

Answer

Yes, f has an inverse. $f^{-1}(1)=4$, $f^{-1}(3)=5.$

Work Step by Step

The graph passes the Horizontal Line Test (any horizontal line that intersects the graph, does so in only one point). The function is one-to-one and has an inverse. If (a,b) is on the graph, this means that $f(a)=b$ and $f^{-1}(b)=a.$ The point $(4,1)$ is on the graph, so $f^{-1}(1)=4.$ The point $(5,3)$ is on the graph, so $f^{-1}(3)=5.$
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