Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.3 Exercises - Page 345: 84

Answer

The graph of the inverse function is a reflection of that of the original function in the graph of the identity function (y =x)

Work Step by Step

Graph of $f^{-1}$ is a reflection of the graph of $f$ in the line described by y=x. Let the graph of $f$ contain a point, say (a, b) then -and only then- the graph of $f^{-1}$ will contain the point (b, a). This is so because if the graph of $f$ contain (a, b), that means $ f(a) = b$ which implies $f^{-1}(b)=a$ which in turn implies that the graph of $f^{-1}$ will contain the point (b, a)
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