Question

Pls help I dont understand. Find the inverse of this function.

Answer 1

In the inverse we replace the place of x by y .

`g(x) = \sqrt[3]{x} - 3 \\ \\ x = \sqrt[3]{y} - 3 \\ \sqrt[3]{y} = x + 3 \\ y = {(x + 3)}^(3) \\ y = {(x + 3)}^(2) (x + 3) \\ y = ({x}^(2) + 6x + 9)(x + 3) \\ \\ y = {x}^(3) + 6 {x}^(2) + 9x + 3 {x}^(2) + 18x + 27 \\ \\ y = {x}^(3) + 9 {x}^(2) + 27x + 27 \\ \\ \\ g(x)^( - 1) = {x}^(3) + 9 {x}^(2) + 27x + 27`

I hope I helped you^_^