College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 2 - Functions and Graphs - Exercise Set 2.7 - Page 309: 17


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

Work Step by Step

${y}$=${x}^{3}$+2 Switch x and y then solve for y to find inverse: ${x}$=${y}^{3}$+2 ${x-2}$=${y}^{3}$ $\sqrt[3] {x-2}$=${y}$=${f}^{-1}$ ${f}^{-1}$($f{(x)}$)=x ${f}^{-1}$($f{(x)}$)=$\sqrt[3] {{x}^{3}+2-2}$ ${f}^{-1}$($f{(x)}$)=$\sqrt[3] {{x}^{3}}$ ${f}^{-1}$($f{(x)}$)=x
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