I thought the definition and notation for a function was $f(x)$ or $f(x,y)$ and so on for a multivariable function. However I have also seen this definition $$f(x,y,y')$$ which I think in explicit form is$f(x,y(x),y'(x))$, i.e. $y$ is a function of $x$. Is it correct? You can see an exemple here (first equation).
So if I'm given a function, say $f(x,y)=y+2x$, how do I know we don't actually mean $f(x,y(x))=y(x)+2x$?
Have I missed something or why this ambiguous definition/notation?