Converting implicit function to explicit

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Converting an implicit function like x + ln(y)/y^2 = 0 into an explicit form y = f(x) is challenging and may not always be possible. Some participants suggest that while it can be expressed as x = g(y), this does not fulfill the requirement for an explicit function. The discussion highlights that certain mathematical techniques may not yield a straightforward solution for y in terms of x. The feasibility of conversion depends on specific conditions and restrictions of the function. Overall, the consensus leans towards the difficulty of achieving an explicit form from the given implicit function.
JulieK
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I have an implicit function [e.g. x+\frac{ln(y)}{y^2}=0)]. Is there any mathematical trick/technique that can convert this to an explicit function (i.e. y=f(x)) even within certain restrictions and conditions.
 
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JulieK said:
I have an implicit function [e.g. x+\frac{ln(y)}{y^2}=0)]. Is there any mathematical trick/technique that can convert this to an explicit function (i.e. y=f(x)) even within certain restrictions and conditions.
I don't believe so. It would be simple to write as x = g(y), though. What's wrong with that?
 

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