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About: Comparametric equation     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:WikicatEquations, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)

Type: yago:Abstraction100002137yago:Communication100033020yago:Equation106669864yago:MathematicalStatement106732169yago:Message106598915yago:Statement106722453yago:WikicatEquations New Facet based on Instances of this Class

A comparametric equation is an equation that describes a parametric relationship between a function and a dilated version of the same function, where the equation does not involve the parameter. For example, ƒ(2t) = 4ƒ(t) is a comparametric equation, when we define g(t) = ƒ(2t), so that we have g = 4ƒ no longer contains the parameter, t. The comparametric equation g = 4ƒ has a family of solutions, one of which is ƒ = t2. To see that ƒ = t2 is a solution, we merely substitute back in: g = ƒ(2t) = (2t)2 = 4t2 = 4ƒ, so that g = 4ƒ.