How to identify whether a function is implicit or explicit?

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Homework Help Overview

The discussion revolves around identifying whether a function is implicit or explicit, particularly through the examination of a specific equation involving variables x and y. Participants explore definitions and examples to clarify the distinction between implicit and explicit functions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the definitions of implicit and explicit functions, with some providing examples and questioning the classification of a specific equation. There is an exploration of whether the equation can be rearranged to express y as a function of x.

Discussion Status

The conversation is ongoing, with participants offering definitions and examples while questioning the implications of rearranging the given equation. There is no explicit consensus, as differing interpretations of the function's classification are being explored.

Contextual Notes

Participants are working within the constraints of algebraic manipulation to determine the nature of the function, and there is an emphasis on the need for further algebraic verification to support their claims.

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how to identify whether a function is implicit or explicit?
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If a function is written (or can be written) as y=f(x) then it is explicit, if it only has the form f(x,y)=0 for example then it is implicit.
 


hunt_mat said:
If a function is written (or can be written) as y=f(x) then it is explicit, if it only has the form f(x,y)=0 for example then it is implicit.

suppose the equation is x^2/3 + y^2/3 = a^2/3. Is it a implicit function or explicit?
 


The equation can be written as:
[tex] x^{\frac{2}{3}}+y^{\frac{2}{3}}-a^{\frac{2}{3}}=0[/tex]
So according to my definition, it is implicit. The next question is is, can it be re-arranged to give y=f(x) for some f(x), this requires algebra to check and this is your job.
 


hunt_mat said:
The equation can be written as:
[tex] x^{\frac{2}{3}}+y^{\frac{2}{3}}-a^{\frac{2}{3}}=0[/tex]
So according to my definition, it is implicit. The next question is is, can it be re-arranged to give y=f(x) for some f(x), this requires algebra to check and this is your job.

but the function canbe written as y^2/3= a^2/3 - x^2/3.
so it should be explicit. how implicit?
 


No, not just y^n, but y. If we take the roots then
[tex] y=\pm (a^{\frac{2}{3}}-x^{\frac{2}{3}})^{\frac{3}{2}}[/tex]
Why is this not a well defined function?
 

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