Question

HURRY ASAP ?!?!?!?!?!?!?!?Which of the following is the inverse of

Answer 1

`f^(-1)(x) = \sqrt[3]{(x -4)/(5)} +2`

Explanation:

Given

`f(x) = 5(x - 2)^3 + 4`

Required

Determine the inverse

`f(x) = 5(x - 2)^3 + 4`

Replace f(x) with y

`y = 5(x - 2)^3 + 4`

Swap the positions of x and y

`x = 5(y - 2)^3 + 4`

Make y the subject

`x -4= 5(y - 2)^3`

Divide by 5

`(x -4)/(5)= (y - 2)^3`

Take cube roots of both sides

`\sqrt[3]{(x -4)/(5)}= y - 2`

Add 2 to both sides

`\sqrt[3]{(x -4)/(5)} +2 = y`

`y = \sqrt[3]{(x -4)/(5)} +2`

Replace y with
`f^(-1)(x)`

`f^(-1)(x) = \sqrt[3]{(x -4)/(5)} +2`