Question

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

Answer 1

`f^-1(x) = root(7)(x)`

Explanation:

A standard method to find the inverse of a function `f(x)` is to set `y = f(x)` and solve for `x`. The result will be `x = f^-1(y)`

Here, for instance, let `y = x^7`

Then `root(7)(y) = root(7)(x^7) = x`

Thus `f^-1(y) = root(7)(y)`, meaning

`f^-1(x) = root(7)(x)`

(To verify this, check that `f(f^-1(x)) = f^-1(f(x)) = x`)