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Elementary function
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, an elementary function is a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> of a single <a href="/facts/Variable_(mathematics)/VbQlrvKz">variable</a> (typically <a href="/facts/Function_of_a_real_variable/bbNG3DnN">real</a> or <a href="/facts/Complex_analysis/hgCoQlH0">complex</a>) that is defined as taking <a href="/facts/Addition/apFWJBFB">sums</a>, <a href="/facts/Multiplication/VtcUjpNv">products</a>, <a href="/facts/Algebraic_function/yT7EKmwF">roots</a> and <a href="/facts/Composition_of_functions/r5Pvnmth">compositions</a> of <a href="/facts/Finite_set/za1newlP">finitely</a> many <a href="/facts/Polynomial/Lzak8VVx">polynomial</a>, <a href="/facts/Rational_function/2nJGu0Ko">rational</a>, <a href="/facts/Trigonometric_functions/czej7ur0">trigonometric</a>, <a href="/facts/Hyperbolic_functions/Y4Cb5S35">hyperbolic</a>, and <a href="/facts/Exponential_function/ewlYxvR2">exponential</a> functions, and their <a href="/facts/Inverse_function/Tg5nnXlu">inverses</a> (e.g., <a href="/facts/Inverse_trigonometric_functions/bVwU9FPG">arcsin</a>, <a href="/facts/Natural_logarithm/PnreKEzI">log</a>, or <i>x</i>1/<i>n</i>). </p><p>All elementary functions are continuous on their <a href="/facts/Domain_of_a_function/FQvoeUpX">domains</a>. </p><p>Elementary functions were introduced by <a href="/facts/Joseph_Liouville/U22o7wtK">Joseph Liouville</a> in a series of papers from 1833 to 1841. An <a href="/facts/Abstract_algebra/YNNE1CNz">algebraic</a> treatment of elementary functions was started by <a href="/facts/Joseph_Fels_Ritt/4ChIswSR">Joseph Fels Ritt</a> in the 1930s. Many textbooks and dictionaries do not give a precise definition of the elementary functions, and mathematicians differ on it. </p>