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	<title>Template:Functions - Revision history</title>
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	<updated>2026-11-14T02:04:26Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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		<id>https://en.bharatpedia.org/w/index.php?title=Template:Functions&amp;diff=35721&amp;oldid=prev</id>
		<title>WikiDwarf: 1 revision imported</title>
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		<updated>2021-04-25T08:57:48Z</updated>

		<summary type="html">&lt;p&gt;1 revision imported&lt;/p&gt;
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				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 14:27, 25 April 2021&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-notice&quot; lang=&quot;en&quot;&gt;&lt;div class=&quot;mw-diff-empty&quot;&gt;(No difference)&lt;/div&gt;
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		<author><name>WikiDwarf</name></author>
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	<entry>
		<id>https://en.bharatpedia.org/w/index.php?title=Template:Functions&amp;diff=35720&amp;oldid=prev</id>
		<title>&gt;Eagleash: Undid revision 1007916747 by 183.171.19.179 (talk) Reverting vandalism or test edit which produced ref error msgs at pages where the template is used (and here)</title>
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		<updated>2021-02-21T13:39:27Z</updated>

		<summary type="html">&lt;p&gt;Undid revision 1007916747 by &lt;a href=&quot;/wiki/Special:Contributions/183.171.19.179&quot; title=&quot;Special:Contributions/183.171.19.179&quot;&gt;183.171.19.179&lt;/a&gt; (&lt;a href=&quot;/w/index.php?title=User_talk:183.171.19.179&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;User talk:183.171.19.179 (page does not exist)&quot;&gt;talk&lt;/a&gt;) &lt;a href=&quot;/wiki/Help:Reverting&quot; title=&quot;Help:Reverting&quot;&gt;Reverting&lt;/a&gt; &lt;a href=&quot;https://en.bharatpedia.org/wiki/Bharatpedia:Vandalism&quot; class=&quot;extiw&quot; title=&quot;wikipedia:Vandalism&quot;&gt;vandalism&lt;/a&gt; or test edit which produced ref error msgs at pages where the template is used (and here)&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Sidebar&lt;br /&gt;
 | name = Functions&lt;br /&gt;
&lt;br /&gt;
 | titlestyle = letter-spacing:0.0125em; background-color:#FFCC99&lt;br /&gt;
 | title = [[Function (mathematics)|Function]]&lt;br /&gt;
&lt;br /&gt;
 | image = {{math|&amp;#039;&amp;#039;x&amp;#039;&amp;#039; ↦ &amp;#039;&amp;#039;f&amp;#039;&amp;#039;&amp;amp;thinsp;(&amp;#039;&amp;#039;x&amp;#039;&amp;#039;)|size=250%}}&lt;br /&gt;
&lt;br /&gt;
 | headingstyle = font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; text-decoration: overline; padding: 5px 0 3px&lt;br /&gt;
&lt;br /&gt;
 | heading1 = Examples by [[domain of a function|domain]] and [[codomain]]&lt;br /&gt;
 | content1style = text-align: left; padding-left: 1.5em;&lt;br /&gt;
 | content1 = {{plainlist|1=&lt;br /&gt;
* {{nowrap|1=&amp;lt;span title=&amp;quot;arbitrary set&amp;quot; style=&amp;quot;color:gray; padding-right: 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;X&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt; &amp;lt;!-- space before comment deliberate&lt;br /&gt;
--&amp;gt;&amp;lt;span style=&amp;quot;font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em&amp;quot;&amp;gt;[[Boolean-valued function|→]]&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;Boolean codomain&amp;quot; style=&amp;quot;padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;B&amp;#039;&amp;#039;&amp;#039;,}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;Boolean domain&amp;quot; style=&amp;quot;padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;B&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span style=&amp;quot;font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em&amp;quot;&amp;gt;[[Ordered pair|→]]&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;arbitrary set&amp;quot; style=&amp;quot;color:gray; padding: 0 0.3em;&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;X&amp;#039;&amp;#039;&amp;#039;,}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;several Boolean variables, or finite Boolean algebra&amp;quot; style=&amp;quot;padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;B&amp;#039;&amp;#039;&amp;#039;&amp;lt;sup&amp;gt;&amp;#039;&amp;#039;n&amp;#039;&amp;#039;&amp;lt;/sup&amp;gt;}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span style=&amp;quot;font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em&amp;quot;&amp;gt;[[Boolean function|→]]&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;Boolean codomain&amp;quot; style=&amp;quot;padding-left: 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;B&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt;}}&lt;br /&gt;
* {{nowrap|1=&amp;lt;span title=&amp;quot;arbitrary set&amp;quot; style=&amp;quot;color:gray; padding-right: 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;X&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span style=&amp;quot;font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em&amp;quot;&amp;gt;[[integer-valued function|→]]&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;integers&amp;quot; style=&amp;quot;padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;Z&amp;#039;&amp;#039;&amp;#039;,}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;integers&amp;quot; style=&amp;quot;padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;Z&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span style=&amp;quot;font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em&amp;quot;&amp;gt;[[sequence|→]]&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;arbitrary set&amp;quot; style=&amp;quot;color:gray; padding-left: 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;X&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt;}}&lt;br /&gt;
* {{nowrap|1=&amp;lt;span title=&amp;quot;arbitrary set&amp;quot; style=&amp;quot;color:gray; padding-right: 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;X&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span style=&amp;quot;font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em&amp;quot;&amp;gt;[[real-valued function|→]]&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;real numbers&amp;quot; style=&amp;quot;padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;R&amp;#039;&amp;#039;&amp;#039;,}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;real numbers&amp;quot; style=&amp;quot;padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;R&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span style=&amp;quot;font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em&amp;quot;&amp;gt;[[function of a real variable|→]]&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;arbitrary set&amp;quot; style=&amp;quot;color:gray; padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;X&amp;#039;&amp;#039;&amp;#039;,}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;real coordinate (or Euclidean) space&amp;quot; style=&amp;quot;padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;R&amp;#039;&amp;#039;&amp;#039;&amp;lt;sup&amp;gt;&amp;#039;&amp;#039;n&amp;#039;&amp;#039;&amp;lt;/sup&amp;gt;}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span style=&amp;quot;font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em&amp;quot;&amp;gt;[[function of several real variables|→]]&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;arbitrary set&amp;quot; style=&amp;quot;color:gray; padding-left: 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;X&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt;}}&lt;br /&gt;
* {{nowrap|1=&amp;lt;span title=&amp;quot;arbitrary set&amp;quot; style=&amp;quot;color:gray; padding-right:0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;X&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span style=&amp;quot;font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em&amp;quot;&amp;gt;[[complex-valued function|→]]&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;complex numbers&amp;quot; style=&amp;quot;padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;C&amp;#039;&amp;#039;&amp;#039;,}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;complex numbers&amp;quot; style=&amp;quot;padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;C&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span style=&amp;quot;font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em&amp;quot;&amp;gt;[[function of a complex variable|→]]&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;arbitrary set&amp;quot; style=&amp;quot;color:gray; padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;X&amp;#039;&amp;#039;&amp;#039;,}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;complex coordinate space&amp;quot; style=&amp;quot;padding: 0 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;C&amp;#039;&amp;#039;&amp;#039;&amp;lt;sup&amp;gt;&amp;#039;&amp;#039;n&amp;#039;&amp;#039;&amp;lt;/sup&amp;gt;}}&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span style=&amp;quot;font-size:150%; letter-spacing:-0.125em; padding: 0 0.3em&amp;quot;&amp;gt;[[several complex variables|→]]&amp;lt;/span&amp;gt; &amp;lt;!--&lt;br /&gt;
--&amp;gt;&amp;lt;span title=&amp;quot;arbitrary set&amp;quot; style=&amp;quot;color:gray; padding-left: 0.3em&amp;quot;&amp;gt;{{math|&amp;#039;&amp;#039;&amp;#039;X&amp;#039;&amp;#039;&amp;#039;}}&amp;lt;/span&amp;gt;}}&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
 | heading2 = [[function space|Classes/properties]] &lt;br /&gt;
 | content2 = {{flatlist|&lt;br /&gt;
* [[Constant function|Constant]]&lt;br /&gt;
* [[Identity function|Identity]]&lt;br /&gt;
* [[Linear map|Linear]]&lt;br /&gt;
* [[Polynomial]]&lt;br /&gt;
* [[Rational function|Rational]]&lt;br /&gt;
* [[Algebraic function|Algebraic]]&lt;br /&gt;
* [[Analytic function|Analytic]]&lt;br /&gt;
* [[Smooth function|Smooth]]&lt;br /&gt;
* [[Continuous function|Continuous]]&lt;br /&gt;
* [[Measurable function|Measurable]]&lt;br /&gt;
* [[Injective function|Injective]]&lt;br /&gt;
* [[Surjective function|Surjective]]&lt;br /&gt;
* [[Bijection|Bijective]]&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
 | heading3 =  Constructions&lt;br /&gt;
 | content3 = {{flatlist|&lt;br /&gt;
* [[Restriction (mathematics)|Restriction]]&lt;br /&gt;
* [[function composition|Composition]]&lt;br /&gt;
* [[Lambda calculus|λ]]&lt;br /&gt;
* [[Inverse function|Inverse]]&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
 | heading4 =  Generalizations  &lt;br /&gt;
 | content4 = {{flatlist|&lt;br /&gt;
* [[Partial function|Partial]]&lt;br /&gt;
* [[Multivalued function|Multivalued]]&lt;br /&gt;
* [[Implicit function|Implicit]]&lt;br /&gt;
}}&lt;br /&gt;
}}&amp;lt;noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
{{Math templates|boxes}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics sidebar templates]]&lt;br /&gt;
&amp;lt;/noinclude&amp;gt;&lt;/div&gt;</summary>
		<author><name>&gt;Eagleash</name></author>
	</entry>
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