Question

Question #d5779

Answer 1

Substitute `f^-1(x)` for x
Use the property `f(f^-1(x)) = x`
Solve for `f^-1(x)`

Explanation:

Given: `f(x) = root3(x/7) -9`

Substitute `f^-1(x)` for every x:

`f(f^-1(x)) = root3(f^-1(x)/7) -9`

Use the property `f(f^-1(x)) =x`:

`x= root3(f^-1(x)/7) -9`

Add 9 to both sides:

`x+9= root3(f^-1(x)/7)`

Cube both sides:

`(x+9)^3= f^-1(x)/7`

Multipy both sides by 7:

`f^-1(x)=7(x+9)^3`