Definition confusion:
I wish to show that $f(x,y)={-y\over x}$ and $g(x,y)=\log |x|$ are functionally independent on some domain.
What does that mean? What do I have to show? And how does one choose the domain?
Thank you.
This is related to question 2 on P. 84 in this book. In particular, the note in the square brackets. However, I don't know what exactly that is and why we would like to do that.