# What is an implicit function?

• B
Would you please explain what an implicit function in general is? Why ##y^2+x^2=c## is assumed as implicit even though it can be expressed in terms of ##y##?

##y^2=c-x^2## and then ##y=\sqrt |x|##

Thank you.

QuantumQuest
Gold Member
In general, any function we get by taking a relation ##f(x,y) = g(x,y)## and solving for ##y## is called an implicit function for the relation at hand. But keep in mind that a relation may have more than one implicit function. The example you give i.e. ##x^2 + y^2 = c## has more than one implicit function. If you solve for ##y^2## as you did and you want to get ##y##, you need to take the square root of the right hand side and this leads to one positive square root (one implicit function) and one negative (a second implicit function) for any value you give to ##c##.

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