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===Notation===
While the notation {{math|''f''<sup> −1</sup>(''x'')}} might be misunderstood,<ref name=":2" /> {{math|(''f''(''x''))<sup>−1</sup>}} certainly denotes the [[multiplicative inverse]] of {{math|''f''(''x'')}} and has nothing to do with the inverse function of {{mvar|f}}.<ref name="Cajori_1929"/> The notation <math>f^{\langle -1\rangle}</math> might be used for the inverse function to avoid ambiguity with the [[multiplicative inverse]].<ref>Helmut Sieber und Leopold Huber: ''Mathematische Begriffe und Formeln für Sekundarstufe I und II der Gymnasien.'' Ernst Klett Verlag.</ref>
In keeping with the general notation, some English authors use expressions like {{math|sin<sup>−1</sup>(''x'')}} to denote the inverse of the sine function applied to {{mvar|x}} (actually a [[#Partial inverses|partial inverse]]; see below).<ref>{{harvnb|Thomas|1972|loc=pp. 304–309}}</ref><ref name="Cajori_1929"/> Other authors feel that this may be confused with the notation for the multiplicative inverse of {{math|sin (''x'')}}, which can be denoted as {{math|(sin (''x''))<sup>−1</sup>}}.<ref name="Cajori_1929"/> To avoid any confusion, an [[inverse trigonometric function]] is often indicated by the prefix "[[arc (function prefix)|arc]]" (for Latin {{lang|la|arcus}}).<ref name="Korn_2000"/><ref name="Atlas_2009"/> For instance, the inverse of the sine function is typically called the [[arcsine]] function, written as {{math|[[arcsin]](''x'')}}.<ref name="Korn_2000"/><ref name="Atlas_2009"/> Similarly, the inverse of a [[hyperbolic function]] is indicated by the prefix "[[ar (function prefix)|ar]]" (for Latin {{lang|la|ārea}}).<ref name="Atlas_2009"/> For instance, the inverse of the [[hyperbolic sine]] function is typically written as {{math|[[arsinh]](''x'')}}. <ref name="Atlas_2009"/> Note that the expressions like {{math|sin<sup>−1</sup>(''x'')}} can still be useful to distinguish the [[Multivalued_function|multivalued]] inverse from the partial inverse: <math>\sin^{-1}(x) = \{(-1)^k \arcsin(x) + \pi n : n \in \mathbb Z\}</math>. Other inverse special functions are sometimes prefixed with the prefix "inv", if the ambiguity of the {{math|''f''<sup> −1</sup>}} notation should be avoided.<ref name="Hall_1909"/><ref name="Atlas_2009"/>
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