Find the inverse of the radical function \sqrt[3]{x-2}

Question

Find the inverse of the radical function
`\sqrt[3]{x-2}`

Answer 1

f^-1(x)=x^3+2

Explanation:

Answer 2

Answer: y=x³+2 or f⁻¹(x)=x³+2

Explanation:

To find the inverse of the radical function, we replace y with x and x with y. Then, you solve for y.

`y=\sqrt[3]{x-2}` [replace y with x and x with y]

`x=\sqrt[3]{y-2}` [cube both sides to cancel out the cubed root]

`x^3=y-2` [add both sides by 2]

`x^3+2=y`

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.