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Suppose that a function $f$ defined on $\mathbb{R} ^2$ satisfies the following conditions:

$$\begin{array} &f(x+t,y) & = & f(x,y)+ty, \\ f(x,t+y) & = & f(x,y)+ tx \text{ and } \\ f(0,0) & = & K, \text{ a constant.} \end{array}$$

Then for all $x,y \in \mathbb{R}, \:f(x,y)$ is equal to

1. $K(x+y)$
2. $K-xy$
3. $K+xy$
4. none of the above
in Calculus
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