Def. An implicit function is a function that is defined implicitly by an implicit equation, by associating one of the variables (the value) with the others (the arguments). For example, $$F(x,y)=0$$$$ e^x+x+y-\sin(y)=0$$ Def. A transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. For example, $$e^x-y=0$$
Can we state that
- all transcendental functions of more than one variable are implicit functions
and vice versa
- all implicit functions are transcendental functions of more than one variable
Note. I understand that the 1. point is incorrect, but if throw out "all", under what conditions will the 1. point be true?