Question

How do you find the inverse of `g(x)=x^3-1`?

Answer 1

`g^(-1)(x) = root(3)(x+1)`

Explanation:

To find the inverse of a function, we can let `y = f(x)` and then solve for `x` to obtain `x = f^(-1)(y)`.
(Note that it should make sense as to why that is the inverse function obtained, as applying it to the original function `y=f(x)` returns `x`)

Applying this here:

Let `y = g(x) = x^3 - 1`

`=> y+1 = x^3`

`=> root(3)(y+1) = x`

Thus we get `g^(-1)(y) = root(3)(y+1)` meaning

`g^(-1)(x) = root(3)(x+1)`