So by definition, for $ye^y=c$, $W(c)$ is the set(let's say A) of all solutions which satisfy y. I want to find what is $n(A)$
Here's what I got: Let $f(x)e^{f(x)}=c$, then $n(B)$ where $B$ is $A\cap \mathbb{R}$ (I don't know if that's the correct notation but I mean set B are the real solutions of $W(x)$ ) is
If f(x) is 1 degree polynomial=1
If f(x) is 2 degree polynomial=0 or 2
If f(x) is 1 degree polynomial=1 or 3
(This is a good one)If f(x) is 4 degree polynomial=0 or 2 or 3 or 4
Like this.
My question: what is $n(A) and n(B)$ and why?