This simply means that f is a function of u and v, which becomes a function of x and y when you substitute u=ax+by and v=bx-ay in the definition of f. (It does not mean that the formula for f as a function of x and y is the same as the formula for f as a function of u and v.)

To give a concrete example, if then . You may think that this is a bad and confusing notation (so do I), but that has to be what the question means. Once you interpret it that way, the question becomes an easy exercise in using the chain rule.