For which of the following functions is ~$f\left ( a+b \right )=f\left ( a \right )+f\left ( b \right )$~ for all positive numbers a and b ?


~$f\left ( x \right )=x^{2}$~

~$f\left ( x \right )=x+1$~

~$f\left ( x \right )=\sqrt{x}$~

~$f\left ( x \right )=\frac{2}{x}$~

~$f\left ( x \right )=-3x$~

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Prep2007E1-PS