Finding the Inverse of $f(x) = \frac x{2^x}$

Question

How does one find the inverse of the equation:

$$ f(x) = \frac{x}{2^x} $$

for the least possible output value?

Answer 1

Hint. You may write $$ \frac{x}{2^x}=z $$ or $$ -(x\ln 2)\:e^{-(x\ln 2)}=-z \ln 2 $$ then have a look at the Lambert function $W(\cdot)$: here or here.

Answer 2

$$ y = \dfrac{x}{2^x} $$

$$ x = \dfrac{y}{2^y} $$

writing y as a function of x is difficult, if not impossible.