Problem

The key is to recognize that $f$ is defined on a transformed pair of inputs, not the standard $(x, y)$ directly. To find the explicit form of $f$, treat the arguments $u = x + ay$ and $v = x - ay$ as new variables, then solve for $x$ and $y$ in terms of $u$ and $v$. Once you express the right side $axy$ in terms of $u$ and $v$, you'll have $f(u, v)$ in its standard form—which is exactly what $f(x, y)$ equals.

The key is to recognize that $f$ is defined on a transformed pair of inputs, not the standard $(x, y)$ directly. To find the explicit form of $f$, treat the arguments $u = x + ay$ and $v = x - ay$ as new variables, then solve for $x$ and $y$ in terms of $u$ and $v$. Once you express the right side $axy$ in terms of $u$ and $v$, you'll have $f(u, v)$ in its standard form—which is exactly what $f(x, y)$ equals.