Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Review - Test - Page 236: 15

Answer

a) $f^{-1}(x)=3-x^2$ b) see graph

Work Step by Step

To find the inverse of a function, one must swap places of $x$ and $f(x)$ and then solve for $f(x)$ $f(x)=\sqrt{3-x}$ Swap places $x=\sqrt{3-f(x)}$ Solve for $f(x)$ by first squaring both sides $x^2=(\sqrt{3-f(x)})^2$ $x^2=3-f(x)$ Add $f(x)$ to both sides and subtract $x^2$ from both sides as well $x^2+f(x)-x^2=3-f(x)+f(x)-x^2$ Simplify $f(x)=3-x^2$ Since the range of the original function is [0, ∞), the domain of the inverse function is [0, ∞) as it appears on the graph.
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