Question

Find the inverse of the function. f(x) = the cube root of quantity x divided by six. - 7

Answer 1

`f^(-1)(x)=6(x+7)^(3)`

Explanation:

we have

`f(x)=\sqrt[3]{(x)/(6)}-7`

Let

`y=f(x)\\ y=\sqrt[3]{(x)/(6)}-7`

Exchanges the variable x for y and y for x

`x=\sqrt[3]{(y)/(6)}-7`

Isolate the variable y

`x+7=\sqrt[3]{(y)/(6)}`

elevates to the cube both members

`(x+7)^(3)=(y)/(6) \\ \\y=6(x+7)^(3)`

Let

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

`f^(-1)(x)=6(x+7)^(3)` ------> inverse function