How to identify whether a function is implicit or explicit?

[amaresh92]

how to identify whether a function is implicit or explicit?
advanced thanks.

 

[hunt_mat]

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.

 

[amaresh92]

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?

 

[hunt_mat]

The equation can be written as:
$$x^{\frac{2}{3}}+y^{\frac{2}{3}}-a^{\frac{2}{3}}=0$$
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.

 

[amaresh92]

The equation can be written as:
$$x^{\frac{2}{3}}+y^{\frac{2}{3}}-a^{\frac{2}{3}}=0$$
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?

 

[hunt_mat]

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