A function \( f: \mathrm{R} \rightarrow \mathrm{R} \) is defined by \[ \begin{array}{l} f(x+y)-k...

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A function \( f: \mathrm{R} \rightarrow \mathrm{R} \) is defined by
\[
\begin{array}{l}
f(x+y)-k x y=f(\mathrm{x})+2 y^{2} \forall x, y \in \mathrm{R} \\
\text { and } f(1)=2 ; f(2)=8
\end{array}
\]
where \( k \) is some constant, the \( f(x+y) \cdot f\left(\frac{1}{x+y}\right) \) equal to: (where \( x+y \neq 0 \) )
(a) 1
(b) 4
(c) \( k \)
(d) \( f(1) \)
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