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 - Page 36: 34

Answer

$f(x)=\sqrt{3-x}$ $f^{-1}(x)=3-x^{2}$

Work Step by Step

$f(x)=\sqrt{3-x}$, for $x\le3$ Substitute $f(x)$ by $y$: $y=\sqrt{3-x}$ Solve the equation for $x$. Start by squaring both sides: $y^{2}=(\sqrt{3-x})^{2}$ $y^{2}=3-x$ Take $x$ to the left side and $y^{2}$ to the right side: $x=3-y^{2}$ Interchange $x$ and $y$: $y=3-x^{2}$ Substitute $y$ by $f^{-1}(x)$: $f^{-1}(x)=3-x^{2}$ The graph of both the original function and its inverse is shown in the answer section.
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