File:Finding real part of Lamber W.png

English: Graph of the function ${\displaystyle y=xe^{x}}$ has been plotted by blue color. Lambert W function is defined as the inverse of this function which can be plotted by switching the roles of ${\displaystyle x}$ and ${\displaystyle y}$, or equivalently by reflecting the graph with respect to the line ${\displaystyle y=x}$. Note that Lambert W is not a function, because on part of its domain, it is sending an element of the domain to more than one number in the codomain. To make it a function, one should restrict the codomain (similar to what one does with the square root function). The graph of the multivalued function Lambert W is shown in red color.