How do you find the inverse of the following function $$f(x) = \frac{\ln (x)}{x}$$
What looked like a simple question made my head hurt during exam.
2026-03-26 20:44:10.1774557850
Finding inverse of $f(x) =\frac{\ln(x)}{x}$
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See Lambert's W-function $$ xy = \ln y \Rightarrow e^{xy} = y \Rightarrow -xye^{-xy} = -x \Rightarrow W(-x) = -yx \Rightarrow y = -\frac{W(-x)}{x} $$