A specific property of a given function:

(1)	$\begin{array}{l}\displaystyle F(a_1 \cdot x_1 + a_2 \cdot x_2) = a_1 \cdot F(x_1) + a_2 \cdot F(x_2)\end{array}$

In general case:

(2)	$\begin{array}{l}\displaystyle F \left( \sum_{i=1}^N a_i \cdot x_i \right) = \sum_{i=1}^N a_i \cdot F(x_1)\end{array}$

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See also