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: 19


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

Work Step by Step

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