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Basic examples

Elementary functions of a single variable x include:

Certain elementary functions of a single complex variable z, such as z {\displaystyle {\sqrt {z}}} and log z {\displaystyle \log z}, may be multivalued. Additionally, certain classes of functions may be obtained by others using the final two rules. For example, the exponential function e z {\displaystyle e^{z}} composed with addition, subtraction, and division provides the hyperbolic functions, while initial composition with i z {\displaystyle iz} instead provides the trigonometric functions.