Function composition: Difference between revisions
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A '''composite function''', or '''composition''' of one function on another, represents the result (value) of one [[function]] used as the parameter of another. |
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Describe the new page here. |
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In the expression f(g(x)), the value of g is the parameter of f, and the function f is composed on g. An equivalent representation is (f.g)(x). f.g is a function which is the composite function of f on g. |
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[[derivative|Derivative]]s of compositions involving differentiable functions can always be found using the [[chain rule]]. |
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The composition of a function on itself, such as f.f, is customarily written f<sup>2</sup>. (f.f)(x)=f(f(x))=f<sup>2</sup>(x). Likewise, (f.f.f)(x)=f(f(f(x)))=f<sup>3</sup>(x). |
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In some cases, an expression for f in g(x)=f<sup>r</sup>(x) can be derived from the rule for g given non-integer values of r. This is called [[fractional iteration]]. |
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Revision as of 22:37, 13 March 2003
A composite function, or composition of one function on another, represents the result (value) of one function used as the parameter of another.
In the expression f(g(x)), the value of g is the parameter of f, and the function f is composed on g. An equivalent representation is (f.g)(x). f.g is a function which is the composite function of f on g.
Derivatives of compositions involving differentiable functions can always be found using the chain rule.
The composition of a function on itself, such as f.f, is customarily written f2. (f.f)(x)=f(f(x))=f2(x). Likewise, (f.f.f)(x)=f(f(f(x)))=f3(x).
In some cases, an expression for f in g(x)=fr(x) can be derived from the rule for g given non-integer values of r. This is called fractional iteration.