English: The real parts of the two branches, 0 and -1 of the multivalued function, Lambert W are depicted with the colors blue and red respectively. The domain and image of ${\displaystyle w_{0}}$ as a real function are ${\displaystyle [{\frac {-1}{e}},+\infty )}$, and the domain and image of ${\displaystyle w_{-1}}$ as a real function are ${\displaystyle [{\frac {-1}{e}},0)}$ and ${\displaystyle (-\infty ,-1]}$.