prep07 数学PS63 7612-!-item-!-187;#058&005607

ivanazhou

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

(A) f(x) = x 2
(B) f(x) = x + 1
(C) f(x) = √x
(D) f(x) = 2/x
(E) f(x) = -3x

请教这道题什么思路啊，实在是看不懂啊！谢谢

bb1447

。。。这个。直接带入试试看哪个是满足的不就OK

abhpokemon

就是问你对于所有正整数a,b，下面的函数里面是否符合f(a+b)=f(a)+f(b)
example:
f(x)是否有f(5)=f(2)+f(3)

答案选E，f(5)=-15=f(2)+f(3)=-6-9

jeept

令a=0,就有f(b)=f(0)+f(b),显然f(0)=0;
若a+b=0,就有f(-a)=-f(a)、即f(-x)=-f(x)
可见E满足

ivanazhou

谢谢！可是觉得A 也对的啊 f(x)= x 2
f(2)= 4
f(3)= 6
f(5)= 10

f(5)=f(2)+f(3)= 4+6=10