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 ?
~$f\left ( x \right )=x^{2}$~
~$f\left ( x \right )=x+1$~
~$f\left ( x \right )=\sqrt{x}$~
~$f\left ( x \right )=\frac{2}{x}$~
~$f\left ( x \right )=-3x$~
带入法,A, f(x)=x2, so f(a+b)=(a+b)2 f(a)=a2, f(b)=b2 failed.
B, a+b+1 not equal to a+1+b+1
C:
E: -3(a+b)= -3a-3b
代入即可