Multiple-Valued Function
a function that takes on several values for the same value of the argument. Multiple-valued functions arise when we invert single-valued functions whose values repeat. Thus, the function x2 takes on every positive value twice (for values of the argument differing only in sign); its inverse is the two-valued function 
The function sin x takes on each of its values an infinite number of times; its inverse is the infinite-valued function arcs in x. Multiple-valued functions play an important role in the theory of analytic functions of a complex variable. In the complex domain, 
has n values for any z ≠ 0, and f(z) = ln z, when z ≠ 0, has an infinite number of values.
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