Question

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

Answer 1

`f^(-1)(x)=root(3)(1-y)`

Explanation:

`f(x)=1-x^3`
One method of finding the inverse of function is by changing the function definition.

Here:
`y=1-x^3`

We will now try to write it for x

Adding `x^3` on both sides of equation
`y+x^3=1`
Subtracting `y` from both sides
`x^3=1-y`
Taking cube-root on both sides
`x=root(3)(1-y)`

Hence,
`f^(-1)(x)=root(3)(1-y)`