Max(x,y) and argmax(x,y)

Question

I am writing my report and I got confused on this simple maths concept.

What I need is: I have 2 values i.e x and y and I want to use the maximum of either x or y as my length. So which statement is correct in maths terms.

1. Max(x,y)
2. argmax(x,y)

Answer 1

Yes, $\max(x,y)$ is the maximum of $x$ and $y$, whereas argmax$_{x,y} f(x,y)$ are the values of $x,y$ that maximize the function $f$.