What is the inverse of the function f(x) = x ln x.?

Question

What is the inverse of f(x) = x (ln x), for which x is more than e^(-1).

Thanks

Answer 1

To evaluate f^(-1)(y), form the sequence x_(n+1)=exp(y/x_n) with x_1=1. This sequence will converge to f^(-1)(y) for suitably large values of y.

Answer 2

there is none....the function is NOT one to one

Answer 3

It's not something which can be expressed as elementary functions.

Normally, when solving the inverse, we make f(x) into y.

y = x ln(x)

And then we swap the terms x and y.

x = y ln(y)

And we try to isolate y, which we cannot do.