Question

Find the inverse of the function f(x)=∛(x+2)-5. Please show all work in finding the inverse.

Answer 1

Explanation:

Let
`f(x) = y`

∴
`y = \sqrt[3]{x + 2} -5`

x has to be isolated and made the subject of the formula:

`y + 5 = \sqrt[3]{x + 2}`

Cube is applied to both sides of the equation to get rid of the cube root:

`(y + 5)^(3) = x + 2`

x =
`(y + 5)^(3) -2`

Substitute
`f^(-1) (y) = x`:

`f^(-1) (y) = (y + 5)^(3) - 2`

Replace y with x:

`f^(-1) (x) = (x + 5)^(3) -2`