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: 35

Answer

$f(x)=x^{4}+4$ $f^{-1}(x)=\sqrt[4]{x-4}$
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Work Step by Step

$f(x)=x^{4}+4$, for $x\ge0$ Substitute $f(x)$ by $y$: $y=x^{4}+4$ Solve the equation for $x$. Start by taking $4$ to the left side: $y-4=x^{4}$ Take the fourth root of both sides and rearrange the equation: $\sqrt[4]{y-4}=\sqrt[4]{x^{4}}$ $x=\sqrt[4]{y-4}$ Interchange $x$ and $y$: $y=\sqrt[4]{x-4}$ Substitute $y$ by $f^{-1}(x)$: $f^{-1}(x)=\sqrt[4]{x-4}$ The graph of both the original function and its inverse is shown in the answer section.
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