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Inverse function
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=== Standard inverse functions === The following table shows several standard functions and their inverses: {| class="wikitable" align="center" |+Inverse arithmetic functions |- !scope="col" align="center" | Function {{math|''f''(''x'')}} !scope="col" align="center" | Inverse {{math|''f''<sup>ββ1</sup>(''y'')}} !scope="col" align="center" | Notes |- | align="center" | {{math|''x'' [[addition|+]] ''a''}} | align="center" | {{math|''y'' [[subtraction|β]] ''a''}} | |- | align="center" | {{math|''a'' β ''x''}} | align="center" | {{math|''a'' β ''y''}} | |- | align="center" | {{math|[[multiplication|''mx'']]}} | align="center" | {{sfrac|{{mvar|y}}|{{mvar|m}}}} | {{math|''m'' β 0}} |- | align="center" | {{sfrac|1|{{mvar|x}}}} (i.e. {{math|''x''<sup>β1</sup>}}) | align="center" | {{sfrac|1|{{mvar|y}}}} (i.e. {{math|''y''<sup>β1</sup>}}) | {{math|''x'',β''y'' β 0}} |- | align="center" | {{math|''x''<sup>''p''</sup>}} | align="center" | <math>\sqrt[p]y</math> (i.e. {{math|''y''<sup>1/''p''</sup>}}) | integer {{math|''p'' > 0}}; {{math|''x'',β''y'' β₯ 0}} if {{math|p}} is even |- | align="center" | {{math|''a''<sup>''x''</sup>}} | align="center" | {{math|[[logarithm|log]]<sub>''a''</sub>β''y''}} | {{math|''y'' > 0}} and {{math|''a'' > 0}} and {{math|''a'' β 1}} |- | align="center" | {{math|''x''[[e (mathematical constant)|''e'']]<sup>''x''</sup>}} | align="center" | {{math|[[Lambert W function|W]]β(''y'')}} | {{math|''x'' β₯ β1}} and {{math|''y'' β₯ β1/''e''}} |- | align="center" | [[trigonometric function]]s | align="center" | [[inverse trigonometric function]]s | various restrictions (see table below) |- | align="center" | [[hyperbolic function]]s | align="center" | [[inverse hyperbolic function]]s | various restrictions |}
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