how to identify whether a function is implicit or explicit?
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:
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
Why is this not a well defined function?
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