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: 21


a. $f^{-1}(x) = x/2$ b. $f(f^{-1}(x)) = 2(x/2)$ $f(f^{-1}(x)) = x$ $f^{-1}(f(x)) = 2x/2$ $f^{-1}(f(x)) = x$

Work Step by Step

a. To find the inverse of a function switch $f(x)$ with $x$ and replace $f(x)$ with $f^{-1}(x)$. $f(x) = 2x$ $x = 2f(x)$ $x = 2f^{-1}(x)$ $x/2 = f^{-1}(x)$ $f^{-1}(x) = x/2$ b. $f(f^{-1}(x)) = 2(x/2)$ $f(f^{-1}(x)) = x$ $f^{-1}(f(x)) = 2x/2$ $f^{-1}(f(x)) = x$
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