@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-GXT3JJHT-8
  skos:prefLabel "inverse function rule"@en, "règle de dérivation des fonctions réciproques"@fr ;
  a skos:Concept ;
  skos:broader psr:-BXH41LGM-B .

psr:-BXH41LGM-B
  skos:broader psr:-FF99PJ0L-W ;
  skos:altLabel "reciprocal"@en, "multiplicative inverse"@en ;
  skos:prefLabel "reciprocal function"@en, "fonction inverse"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Fonction_inverse>, <https://en.wikipedia.org/wiki/Multiplicative_inverse> ;
  skos:definition """En mathématiques, la <b>fonction inverse</b> est la fonction qui à tout réel <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle x}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>x</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle x}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\\\\displaystyle x}"></span> non nul associe son inverse, noté <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {\\rac {1}{x}}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>1</mn>             <mi>x</mi>           </mfrac>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {1}{x}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68f89eaf83a3811c69adb4bf1119bafd661a4c08" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.166ex; height:5.176ex;" alt="{\\\\displaystyle {\\rac {1}{x}}}"></span>. Elle se note de la manière suivante :  <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle f:{\\egin{cases}\\\\mathbb {R} ^{*}\\	o \\\\mathbb {R} ^{*}\\\\\\\\x\\\\mapsto f(x)=\\\\displaystyle {\\\\dfrac {1}{x}}.\\\\end{cases}}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>f</mi>         <mo>:</mo>         <mrow class="MJX-TeXAtom-ORD">           <mrow>             <mo>{</mo>             <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false">               <mtr>                 <mtd>                   <msup>                     <mrow class="MJX-TeXAtom-ORD">                       <mi mathvariant="double-struck">R</mi>                     </mrow>                     <mrow class="MJX-TeXAtom-ORD">                       <mo>∗<!-- ∗ --></mo>                     </mrow>                   </msup>                   <mo stretchy="false">→<!-- → --></mo>                   <msup>                     <mrow class="MJX-TeXAtom-ORD">                       <mi mathvariant="double-struck">R</mi>                     </mrow>                     <mrow class="MJX-TeXAtom-ORD">                       <mo>∗<!-- ∗ --></mo>                     </mrow>                   </msup>                 </mtd>               </mtr>               <mtr>                 <mtd>                   <mi>x</mi>                   <mo stretchy="false">↦<!-- ↦ --></mo>                   <mi>f</mi>                   <mo stretchy="false">(</mo>                   <mi>x</mi>                   <mo stretchy="false">)</mo>                   <mo>=</mo>                   <mstyle displaystyle="true" scriptlevel="0">                     <mrow class="MJX-TeXAtom-ORD">                       <mstyle displaystyle="true" scriptlevel="0">                         <mfrac>                           <mn>1</mn>                           <mi>x</mi>                         </mfrac>                       </mstyle>                     </mrow>                     <mo>.</mo>                   </mstyle>                 </mtd>               </mtr>             </mtable>             <mo fence="true" stretchy="true" symmetric="true"></mo>           </mrow>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle f:{\\egin{cases}\\\\mathbb {R} ^{*}\\	o \\\\mathbb {R} ^{*}\\\\\\\\x\\\\mapsto f(x)=\\\\displaystyle {\\\\dfrac {1}{x}}.\\\\end{cases}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5048f005d0d081304f59849496112fcaa9f993e5" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -3.184ex; margin-bottom: -0.321ex; width:21.113ex; height:8.176ex;" alt="{\\\\displaystyle f:{\\egin{cases}\\\\mathbb {R} ^{*}\\	o \\\\mathbb {R} ^{*}\\\\\\\\x\\\\mapsto f(x)=\\\\displaystyle {\\\\dfrac {1}{x}}.\\\\end{cases}}}"> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_inverse">https://fr.wikipedia.org/wiki/Fonction_inverse</a>)"""@fr, """In mathematics, a <b>multiplicative inverse</b> or <b>reciprocal</b> for a number <i>x</i>, denoted by 1/<i>x</i> or <i>x</i><sup>−1</sup>, is a number which when multiplied by <i>x</i> yields the multiplicative identity, 1. The multiplicative inverse of a fraction <i>a</i>/<i>b</i> is <i>b</i>/<i>a</i>. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The <b>reciprocal function</b>, the function <i>f</i>(<i>x</i>) that maps <i>x</i> to 1/<i>x</i>, is one of the simplest examples of a function which is its own inverse (an involution).  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Multiplicative_inverse">https://en.wikipedia.org/wiki/Multiplicative_inverse</a>)"""@en ;
  dc:modified "2024-10-18"^^xsd:date ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:narrower psr:-GXT3JJHT-8 .

psr:-FF99PJ0L-W
  skos:prefLabel "algebraic function"@en, "fonction algébrique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-BXH41LGM-B .