Question

Find the inverse of the function.

Answer 1

f(x) =
`4\sqrt[3]{x} - 8`

Let's replace f(x) with y

y =
`4\sqrt[3]{x} - 8`

Switch the x and y

x =
`4\sqrt[3]{y} - 8`

Now, let's solve for y. Start off by adding 8 to both sides.

x + 8 =
`4\sqrt[3]{y}`

Divide both sides by 4

`(x)/(4) + 2` =
`\sqrt[3]{y}`

Take each side by the power of 3

`((x)/(4) + 2)^(3)` = y

Now, let's replace y with
`f^(-1)(x)`

`f^(-1)(x)` =
`((x)/(4) + 2)^(3)` is the inverse