Inverse function... find the inverse of f(x)=(x^2)exp(x^2) for all x.?

Question

I thought f-inverse didn't exist if f wasn't 1-1 but my homework doesn't think so. Any thoughts?

Answer 1

The inverse is √W(y) where W(y) is the Lambert W-function, defined as the inverse of xe^x. There is no way to express the inverse in terms of classical functions.

If you mean the function (x²)^(x²), that's even worse, and will still involve the W(y) function.

Maybe I'm not reading your expression correctly, or you have it written down wrong?

Answer 2

x = ±√[W(y)]