Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 2 - Review - Concept Check - Page 230: 7

Answer

A graph consists of points (x, f(x)). The y-coordinate is the function value of the x-coordinate. If (3,5) is a point on the graph, then $f(3)=5.$ Also, $f^{-1}(5)=3$

Work Step by Step

A graph consists of points (x, f(x)). The y-coordinate is the function value of the x-coordinate. If (3,5) is a point on the graph, then $f(3)=5.$ Also, if f is one-to-one, then $x=3$ is the only x value that has function value of 5. This means that $f^{-1}(5)=3$, because $f^{-1}(f(x))=x, $ for x=3, $f^{-1}(f(3))=3, $ that is, $f^{-1}(5)=3$
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