Answer: [tex]y=(8x)^{\frac{1}{3}} -1[/tex] or [tex]y=\sqrt[3]{8x} -1[/tex]
Step-by-step explanation:
To find the inverse, you switch y with x and x with y. Then, you solve for y.
[tex]y=\frac{1}{8} (x+1)^3[/tex] [switch y with x and x with y]
[tex]x=\frac{1}{8} (y+1)^3[/tex] [multiply both sides by 8]
[tex]8x=(y+1)^3[/tex] [cube both sides]
[tex]\sqrt[3]{8x} =y+1[/tex] [subtract both sides by 1]
[tex]y=\sqrt[3]{8x} -1[/tex] or [tex]y=(8x)^{\frac{1}{3}} -1[/tex]
