What is an implicit function? Give an example of such function.

Question

What is an implicit function? Give an example of such function.

Answer 1

An implicit function is a function that is defined by an implicit equation. For example if y is a function of x and we know that we have the relation x^2 + y^2 =1 then we say that y is given implicitly. Other examples of such functions are x^4 + y^7 + y^5 +2xy = 0 or ln(y) + e^x = 4xy + x^3 etc.