Answer: y=x³+2 or f⁻¹(x)=x³+2
Step-by-step explanation:
To find the inverse of the radical function, we replace y with x and x with y. Then, you solve for y.
[tex]y=\sqrt[3]{x-2}[/tex] [replace y with x and x with y]
[tex]x=\sqrt[3]{y-2}[/tex] [cube both sides to cancel out the cubed root]
[tex]x^3=y-2[/tex] [add both sides by 2]
[tex]x^3+2=y[/tex]
Now that we have switched the variables and solved for y, we know that the inverse function is y=x³+2 or f⁻¹(x)=x³+2.
