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: 18


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

Work Step by Step

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