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: 22

Answer

a. $f^{-1}(x) = 4x-4$ b. $f(f^{-1}(x)) = (4x-4)/4 + 1$ $f(f^{-1}(x)) = x - 1 + 1$ $f(f^{-1}(x)) = x$ $f^{-1}(f(x)) = 4(x/4 - 1) + 4$ $f^{-1}(f(x)) = x - 4 + 4$ $f^{-1}(f(x)) = x $

Work Step by Step

a. To find the inverse of a function $f(x)$, switch $f(x)$ with $x$ and replace $f(x)$ with $f^{-1}(x)$ $f(x) = x/4 + 1$ $x = f^{-1}(x)/4 + 1$ $x - 1 = f^{-1}(x)/4$ $4x-4 = f^{-1}(x)$ $f^{-1}(x) = 4x-4$ b. $f(f^{-1}(x)) = (4x-4)/4 + 1$ $f(f^{-1}(x)) = x - 1 + 1$ $f(f^{-1}(x)) = x$ $f^{-1}(f(x)) = 4(x/4 - 1) + 4$ $f^{-1}(f(x)) = x - 4 + 4$ $f^{-1}(f(x)) = x $
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