Argument of a function

Argument of a function

In <a href="/en/Mathematics" title="Mathematics" class="wl">mathematics</a>, an argument of a <a href="/en/Function_(mathematics)" title="Function (mathematics)" class="wl">function</a> is a value provided to obtain the function's result. It is also called an <a href="/en/Dependent_and_independent_variables" title="Dependent and independent variables" class="wl">independent variable</a>.<a href="#cite_note-1" style="counter-reset: mw-Ref 1;">[1]</a>

<div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none" about="#mwt1">Input to a mathematical function</div>
<style data-mw-deduplicate="TemplateStyles:r1033289096" typeof="mw:Extension/templatestyles mw:Transclusion">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style>For example, the <a href="/en/Binary_function" title="Binary function" class="wl">binary function</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x,y)=x^{2}+y^{2}}">
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 <annotation encoding="application/x-tex">{\displaystyle f(x,y)=x^{2}+y^{2}}</annotation>
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</math><img loading="lazy"src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41cf50e4a314ca8e2c30964baa8d26e5be7a9386" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:5.328ex; height:2.843ex;" alt="(x,y)">. The <a href="/en/Hypergeometric_function" title="Hypergeometric function" class="wl">hypergeometric function</a> is an example of a four-argument function. The number of arguments that a function takes is called the <a href="/en/Arity" title="Arity" class="wl">arity</a> of the function. A function that takes a single argument as input, such as <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=x^{2}}">
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</math><img loading="lazy"src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84ddac4ae10b1aa4a11741c79771a583419fb1fb" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:9.9ex; height:3.176ex;" alt="f(x)=x^{2}">, is called a <a href="/en/Unary_function" title="Unary function" class="wl">unary function</a>. A function of two or more variables is considered to have a <a href="/en/Domain_of_a_function" title="Domain of a function" class="wl">domain</a> consisting of ordered pairs or <a href="/en/Tuple" title="Tuple" class="wl">tuples</a> of argument values. The argument of a <a href="/en/Circular_function" title="Circular function" class="mw-redirect wl">circular function</a> is an <a href="/en/Angle" title="Angle" class="wl">angle</a>. The argument of a <a href="/en/Hyperbolic_function" title="Hyperbolic function" class="mw-redirect wl">hyperbolic function</a> is a <a href="/en/Hyperbolic_angle" title="Hyperbolic angle" class="wl">hyperbolic angle</a>.

A mathematical function has one or more arguments in the form of independent variables designated in the definition, which can also contain <a href="/en/Parameter#Mathematical_functions" title="Parameter" class="wl">parameters</a>. The independent variables are mentioned in the list of arguments that the function takes, whereas the parameters are not. For example, in the <a href="/en/Logarithmic_function" title="Logarithmic function" class="mw-redirect wl">logarithmic function</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=\log _{b}(x),}">
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</math><img loading="lazy"src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="b"> is considered a parameter. 

Sometimes, <a href="/en/Subscript" title="Subscript" class="mw-redirect wl">subscripts</a> can be used to denote arguments. For example, we can use subscripts to denote the arguments with respect to which <a href="/en/Partial_derivative" title="Partial derivative" class="wl">partial derivatives</a> are taken.<a href="#cite_note-2" style="counter-reset: mw-Ref 2;">[2]</a>

The use of the term "argument" in this sense developed from <a href="/en/Astronomy" title="Astronomy" class="wl">astronomy</a>, which historically used tables to determine the spatial positions of planets from their positions in the sky (<a href="/en/Ephemerides" title="Ephemerides" class="mw-redirect wl">ephemerides</a>). These tables were organized according to measured angles called arguments, literally "that which elucidates something else."<a href="#cite_note-3" style="counter-reset: mw-Ref 3;">[3]</a><a href="#cite_note-4" style="counter-reset: mw-Ref 4;">[4]</a>

In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. For example, the binary function 
  
    
      
        f =
        
          x
          
            2
          
        
        +
        
          y
          
            2
          
        
      
    
    {\displaystyle f =x^{2}+y^{2}}
  
 has two arguments, 
  
    
      
        x
      
    
    {\displaystyle x}
  
 and 
  
    
      
        y
      
    
    {\displaystyle y}
  
, in an ordered pair {\displaystyle }
  
. The hypergeometric function is an example of a four-argument function. The number of arguments that a function takes is called the arity of the function. A function that takes a single argument as input, such as 
  
    
      
        f =
        
          x
          
            2
          
        
      
    
    {\displaystyle f =x^{2}}
  
, is called a unary function. A function of two or more variables is considered to have a domain consisting of ordered pairs or tuples of argument values. The argument of a circular function is an angle. The argument of a hyperbolic function is a hyperbolic angle. A mathematical function has one or more arguments in the form of independent variables designated in the definition, which can also contain parameters. The independent variables are mentioned in the list of arguments that the function takes, whereas the parameters are not. For example, in the logarithmic function 
  
    
      
        f =
        
          log
          
            b
          
        
        ⁡ ,
      
    
    {\displaystyle f =\log _{b} ,}
  
 the base 
  
    
      
        b
      
    
    {\displaystyle b}
  
 is considered a parameter.  