# About of domain of definition of an implicit function [closed]

How to determine the domain of definition of a function $y(x)$ defined implicitly:

$$\Phi(x,y)=0.$$

Example:

1. $y^4+y^2-e^x=0$
2. $y^3+y+\sin(x)=0$

Thanks.

• $y$ has to be a function of $x$, not the other way around – Orest Bucicovschi Oct 23 '17 at 9:59
• $y$ is given implicitly. – Wang Oct 23 '17 at 10:01

Solve the equations for $x$. The image of the function $x=x(y)$ is the maximal domain of definition for the function $y=y(x)$.