staymathematicsMedium,Constant function(Also calledConstant valued function）MeansvalueNo change (i.econstant）Offunction。For example, we have a functionf(x)=4, becausefmappingAny value to 4, sofIs a constant.More generally, for a functionf: A→B, if theAAll withinxandy, bothf(x)=f(y), so,fIs a constant function.
Note that each empty function (domainempty set) pointlessly satisfies the above definition becauseANone inxandysendf(x)andf(y)Different.However, some people believe that if empty functions are included, then constant functions will be easier to define.
aboutPolynomial functionA non-zero constant function is called a polynomial of degree zero.
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Constant functions can be used byComposite functionThe relationship between the two is described in two ways.[2]
The following are equivalent:
f: A→BIs a constant function.For all functionsg, h: C→A, fog=foh("o" means composite function).fThe composition with any other function is still a constant function.The first description of the constant function given above isCategorical theoryinConstant morphismMore general concepts are stimulated and defined by nature.
By definition, a function'sDerivative functionMeasure the relationship between the change of independent variable and the change of function.Then we can get that since the value of the constant function is constant, its derivative is zero.
For example:
IffIs defined in asectionIf the variable is a real number function, then if and only iffWhen the derivative function of is always zero,fIs a constant.yesPreordered setThe constant function isIsotonicandReverse orderOf;Conversely, iffIt is both ordinal and reverse, such asfThe domain of is a lattice, thenfIt must be a constant function.
Other properties of constant functions include:
Any semantic field andAccompany domainThe same constant function isEqual powerOf.any topological space The constant on is continuous.In aConnected setMedium, if and only iffWhen is a constant, it isLocal constant。
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staymathematicsField, twofunctionOfComposite functionIt refers to a function that applies the first function to the parameter, and then applies the second function to the result.
Specifically, given two functionsf:X→Yandg:Y→Z, wherefOfAccompany domainbe equal togThe domain of the (calledf、gComposable）, its composite function, recorded asg∘f, withXTo define a domain,ZTo accompany the domain, and set anyx∈XMap tog(f(x))。Sometimes the compound mark "∘∘∘" is omitted to write directlygf。
g∘fThe "∘" in is called the ring operator.
Composite satisfaction of functionAssociative law: Iff、gComposable,g、hCan be compounded, then:
h∘ (g∘f)=(h∘g) ∘f
The composition of functions can be regarded as a special case of the composition of binary relations.
