Question

How do you find `f^-1(x)` given `f(x)=-1/x^2`?

Answer 1

`f(x)^-1=+-sqrt(-1/x)`

Explanation:

You substitute the x values for the y values

`x=-1/y^2`

Then we rearrange for y

`xy^2=-1`

`y^2=-1/x`

`y=+-sqrt(-1/x)`

Such a function doesn't exist as you can't have a negative root on the `RR` plane. Also it fails the function test as you have two x values corresponding to 1 y value.