Question about linear operator on polynomial space $L:\mathbb{R}[x,y]_{\leq 2} \rightarrow \mathbb{R}[x,y]_{\leq 2}$

Question

I'm trying to find a a matrix of a linear operator defined mapping from the set of real polynomials of two variables of degree less than or equal 2 to itself by the following rule:

$L(f(x,y)) = (x^2 + 1)*f(1,1) + f(-x+y, 2x) - f(x,y)$

This is stupid, but I'm not sure about the $f(-x + y,2x)$ part: if we take, for example, $L(x)$, should $f(-x +y, 2x)$ evaluate to $-x + y$ or to $-x$ and $y = 0$? In other words, in this expression, should we take $y$ from the vector space as a vector or should it evaluate to $y$ that is on the left hand side, inside the polynomial?

Answer 1

If $f(x,y)=x$ then $f(x,y)$ does not depend on the second variable. It just outputs the first coordinate. So $f(-x+y,2x)=-x+y$.