Question

How do you find the inverse of `f(x)=4x^7`?

Answer 1

Solve with respect to `x`

hence

`y=f(x)=4*x^7` hence

`x=(y/4)^(1/7)`

Replace `x` with `y` hence

`y=(x/4)^(1/7)`

or

`f^(-1) (x)=(x/4)^(1/7)`

To test that they are really inverses of each other you need to
find both composite functions `f(f^-1(x))` and `f^-1(f(x))`.
Both of these Must be equal to `x` or else they are not inverses of each other.