ArcSinh[x] >= 0 /; x >= 0 && Element[x, Reals]

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#8805; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> x </mi> <mo> &#8805; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <geq /> <apply> <arcsinh /> <ci> x </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <geq /> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSinh", "[", "x", "]"]], "\[GreaterEqual]", "0"]], "/;", RowBox[List[RowBox[List["x", "\[GreaterEqual]", "0"]], "&&", RowBox[List["x", "\[Element]", "Reals"]]]]]]]]

2001-10-29