If $f(x+2y, x-2y) = xy$,then $f(x, y)$ is equal to

Exactly how many functions $f: \mathbb{Q} \rightarrow \mathbb{Q}$ exist such that $f(x+y) = f(x) + f(y)$ and $f(xy) = f(x)f(y)$ for all $x, y \in \mathbb{Q}$?

Let $f: N \times N \rightarrow N$ be a function such that $f(1,1)=2$,$f(m+1, n)=f(m, n)+2(m+n)$,and $f(m, n+1)=f(m, n)+2(m+n-1)$ for all $m, n \in N$. Find the value of $f(2,2)$.

If $f(x) = x - \frac{1}{x}$,$x \neq 0$,then $3f(x) =$

The number of real linear functions $f(x)$ satisfying $f(f(x))=x+f(x)$ is

If $f: R \rightarrow R$ is defined as $f(x+y)=f(x)+f(y), \forall x, y \in R$ and $f(1)=10$,then,$\sum_{r=1}^n(f(r))^2=$