Question

Which function is the inverse of? (picture below)

Answer 1

B.
`f^(-1) (x)=\sqrt[3]{x} +2`

Explanation:

We are given the function
`f(x)=x^3-6x^2+12x-8`

In order to find the inverse, we will need to swap f(x) for y. And then we will switch the locations of x and y. Then we will solve for y.

`f(x)=x^3-6x^2+12x-8\\\\y=x^3-6x^2+12x-8\\\\x=y^3-6y^2+12y-8\\\\x=(y-2)^3\\\\\sqrt[3]{x} =y-2\\y=\sqrt[3]{x} +2\\\\f^(-1) (x)=\sqrt[3]{x} +2`