"f is a function of [some argument]" is completely correct terminology, specific to mathematics. From Columbia University's page "What does "function of" mean?":
A function defines one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) means that y varies according to whatever value x takes on.
Here, "f is a function of a vector argument," is the mathematically appropriate phrase to express that the function f is defined by an argument that is a vector.
As noted below in the comments, you can leave off "argument" since the "...function of..." construction assumes that the object of "of" is an argument.
Finally, this is a construction particular to the discipline of mathematics, so don't expect native English speakers to be generally familiar with it. (Most people I know understand it perfectly, but most people I know are computer programmers!)